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Acronym
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gee (old: xic)
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Name
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hexacontitetrapeton,
hexacross (β6),
aeroex(id),
hexateral antiprism,
triacontaditeric bipyramid,
octahedral duotegum,
square triotegum,
vertex figure of zee,
Gosset polytope 31,1,
lattice C6 contact polytope (span of its small roots),
equatorial cross-section of vertex-first zee
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Circumradius
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1/sqrt(2) = 0.707107
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Inradius
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1/sqrt(12) = 0.288675
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Lace city
in approx. ASCII-art
|
 ©
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o -- o3o3o3o4o (point)
o h o -- x3o3o3o4o (tac)
o -- o3o3o3o4o (point)
where:
o = o3o3o4o (point)
h = x3o3o4o (hex)
|
|
o3o3o3o x3o3o3o
o3o3o3x o3o3o3o
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x o3o3o o x3o3o
o o3o3x x o3o3o
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x3o o3o o3o x3o
o3o o3x o3x o3o
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Coordinates
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(1/sqrt(2), 0, 0, 0, 0, 0) & all permutations, all changes of sign
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Volume
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1/90 = 0.011111
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Surface
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2 sqrt(3)/15 = 0.230940
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Rel. Roundness
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5 π3/576 = 26.915171 %
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General of army
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(is itself convex)
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Colonel of regiment
|
(is itself locally convex
– uniform polypetal members:
& others)
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Dual
|
ax
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Dihedral angles
(at margins)
|
- at pen between hix and hix: arccos(-2/3) = 131.810315°
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Face vector
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12, 60, 160, 240, 192, 64
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Confer
|
- more general:
-
xPo3o...o3o4o
- related segmentopeta:
-
tacpy
hexasc
octete
squepe
- ambification:
-
rag
- general polytopal classes:
-
Wythoffian polypeta
orthoplex
noble polytopes
segmentopeta
lace simplices
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
-
regular orthoplex On
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External
links
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|
The hexacontitetrapeton allows for a projection into 3D as the overlay of ike and a vertex-inscribed gike, cf. to the right.
In fact this corresponds to the folding of D6 into H3.
Note however that due to this projection the former equivalent 60 edges decompose into 30 smaller ones (of x-ike) plus 30 taller ones (of the inscribed f-gike).
folding D6 into H3
o---o o
\ /
X
/ \
o---o---o
=>
o---o---o
5
Note that the hexacontitetrapeton also can be thought of as the external blend of
8 octetes. Further, the overlay of 2 such fully perpendicular decompositions would amount to the degenerate
segmentoexon xo3oo4oo ox3oo4oo&#x.
Incidence matrix according to Dynkin symbol
x3o3o3o3o4o
. . . . . . | 12 ♦ 10 | 40 | 80 | 80 | 32
------------+----+----+-----+-----+-----+---
x . . . . . | 2 | 60 ♦ 8 | 24 | 32 | 16
------------+----+----+-----+-----+-----+---
x3o . . . . | 3 | 3 | 160 ♦ 6 | 12 | 8
------------+----+----+-----+-----+-----+---
x3o3o . . . ♦ 4 | 6 | 4 | 240 | 4 | 4
------------+----+----+-----+-----+-----+---
x3o3o3o . . ♦ 5 | 10 | 10 | 5 | 192 | 2
------------+----+----+-----+-----+-----+---
x3o3o3o3o . ♦ 6 | 15 | 20 | 15 | 6 | 64
x3o3o3o3o4/3o
. . . . . . | 12 ♦ 10 | 40 | 80 | 80 | 32
--------------+----+----+-----+-----+-----+---
x . . . . . | 2 | 60 ♦ 8 | 24 | 32 | 16
--------------+----+----+-----+-----+-----+---
x3o . . . . | 3 | 3 | 160 ♦ 6 | 12 | 8
--------------+----+----+-----+-----+-----+---
x3o3o . . . ♦ 4 | 6 | 4 | 240 | 4 | 4
--------------+----+----+-----+-----+-----+---
x3o3o3o . . ♦ 5 | 10 | 10 | 5 | 192 | 2
--------------+----+----+-----+-----+-----+---
x3o3o3o3o . ♦ 6 | 15 | 20 | 15 | 6 | 64
o3o3o *b3o3o3x
. . . . . . | 12 ♦ 10 | 40 | 80 | 80 | 16 16
---------------+----+----+-----+-----+-----+------
. . . . . x | 2 | 60 ♦ 8 | 24 | 32 | 8 8
---------------+----+----+-----+-----+-----+------
. . . . o3x | 3 | 3 | 160 ♦ 6 | 12 | 4 4
---------------+----+----+-----+-----+-----+------
. . . o3o3x ♦ 4 | 6 | 4 | 240 | 4 | 2 2
---------------+----+----+-----+-----+-----+------
. o . *b3o3o3x ♦ 5 | 10 | 10 | 5 | 192 | 1 1
---------------+----+----+-----+-----+-----+------
o3o . *b3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | 32 *
. o3o *b3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | * 32
xo3oo3oo3oo3ox&#x → height = 1/sqrt(3) = 0.577350
(hix || inv hix)
o.3o.3o.3o.3o. & | 12 ♦ 5 5 | 10 30 | 10 40 30 | 5 25 50 | 1 6 15 10
---------------------+----+-------+--------+-----------+-----------+-----------
x. .. .. .. .. & | 2 | 30 * ♦ 4 4 | 6 12 6 | 4 12 16 | 1 4 7 4
oo3oo3oo3oo3oo&#x | 2 | * 30 ♦ 0 8 | 0 12 12 | 0 8 24 | 0 2 8 6
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o. .. .. .. & | 3 | 3 0 | 40 * ♦ 3 3 0 | 3 6 3 | 1 3 3 1
xo .. .. .. ..&#x & | 3 | 1 2 | * 120 ♦ 0 3 3 | 0 3 9 | 0 1 4 3
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o. .. .. & ♦ 4 | 6 0 | 4 0 | 30 * * | 2 2 0 | 1 2 1 0
xo3oo .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * 120 * | 0 2 2 | 0 1 2 1
xo .. .. .. ox&#x ♦ 4 | 2 4 | 0 4 | * * 90 | 0 0 4 | 0 0 2 2
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o.3o. .. & ♦ 5 | 10 0 | 10 0 | 5 0 0 | 12 * * | 1 1 0 0
xo3oo3oo .. ..&#x & ♦ 5 | 6 4 | 4 6 | 1 4 0 | * 60 * | 0 1 1 0
xo3oo .. .. ox&#x & ♦ 5 | 4 6 | 1 9 | 0 2 3 | * * 120 | 0 0 1 1
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o.3o.3o. & ♦ 6 | 15 0 | 20 0 | 15 0 0 | 6 0 0 | 2 * * *
xo3oo3oo3oo ..&#x & ♦ 6 | 10 5 | 10 10 | 5 10 0 | 1 5 0 | * 12 * *
xo3oo3oo .. ox&#x & ♦ 6 | 7 8 | 4 16 | 1 8 6 | 0 2 4 | * * 30 *
xo3oo .. oo3ox&#x ♦ 6 | 6 9 | 2 18 | 0 6 9 | 0 0 6 | * * * 20
oxo3ooo3ooo3ooo4ooo&#xt → both heights = 1/sqrt(2) = 0.707107
(pt || pseudo tac || pt)
o..3o..3o..3o..4o.. & | 2 * ♦ 10 0 | 40 0 | 80 0 | 80 0 | 32
.o.3.o.3.o.3.o.4.o. | * 10 ♦ 2 8 | 16 24 | 48 32 | 64 16 | 32
--------------------------+------+-------+-------+--------+--------+---
oo.3oo.3oo.3oo.4oo.&#x & | 1 1 | 20 * ♦ 8 0 | 24 0 | 32 0 | 16
.x. ... ... ... ... | 0 2 | * 40 ♦ 2 6 | 12 12 | 24 8 | 16
--------------------------+------+-------+-------+--------+--------+---
ox. ... ... ... ...&#x & | 1 2 | 2 1 | 80 * ♦ 6 0 | 12 0 | 8
.x.3.o. ... ... ... | 0 3 | 0 3 | * 80 ♦ 2 4 | 8 4 | 8
--------------------------+------+-------+-------+--------+--------+---
ox.3oo. ... ... ...&#x & ♦ 1 3 | 3 3 | 3 1 | 160 * | 4 0 | 4
.x.3.o.3.o. ... ... ♦ 0 4 | 0 6 | 0 4 | * 80 | 2 2 | 4
--------------------------+------+-------+-------+--------+--------+---
ox.3oo.3oo. ... ...&#x & ♦ 1 4 | 4 6 | 6 4 | 4 1 | 160 * | 2
.x.3.o.3.o.3.o. ... ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 32 | 2
--------------------------+------+-------+-------+--------+--------+---
ox.3oo.3oo.3oo. ...&#x & ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 | 64
qo ox3oo3oo3oo4oo&#zx → height = 0
(tegum sum of q-line and perp tac)
(tegum product of q-line with tac)
o. o.3o.3o.3o.4o. | 2 * ♦ 10 0 | 40 0 | 80 0 | 80 0 | 32
.o .o3.o3.o3.o4.o | * 10 ♦ 2 8 | 16 24 | 48 32 | 64 16 | 32
---------------------+------+-------+-------+--------+--------+---
oo oo3oo3oo3oo4oo&#x | 1 1 | 20 * ♦ 8 0 | 24 0 | 32 0 | 16
.. .x .. .. .. .. | 0 2 | * 40 ♦ 2 6 | 12 12 | 24 8 | 16
---------------------+------+-------+-------+--------+--------+---
.. ox .. .. .. ..&#x | 1 2 | 2 1 | 80 * ♦ 6 0 | 12 0 | 8
.. .x3.o .. .. .. | 0 3 | 0 3 | * 80 ♦ 2 4 | 8 4 | 8
---------------------+------+-------+-------+--------+--------+---
.. ox3oo .. .. ..&#x ♦ 1 3 | 3 3 | 3 1 | 160 * | 4 0 | 4
.. .x3.o3.o .. .. ♦ 0 4 | 0 6 | 0 4 | * 80 | 2 2 | 4
---------------------+------+-------+-------+--------+--------+---
.. ox3oo3oo .. ..&#x ♦ 1 4 | 4 6 | 6 4 | 4 1 | 160 * | 2
.. .x3.o3.o3.o .. ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 32 | 2
---------------------+------+-------+-------+--------+--------+---
.. ox3oo3oo3oo ..&#x ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 | 64
ooo3ooo3ooo *b3ooo3oxo&#xt → both heights = 1/sqrt(2) = 0.707107
(pt || pseudo tac || pt)
o..3o..3o.. *b3o..3o.. & | 2 * ♦ 10 0 | 40 0 | 80 0 | 80 0 0 | 16 16
.o.3.o.3.o. *b3.o.3.o. | * 10 ♦ 2 8 | 16 24 | 48 32 | 64 8 8 | 16 16
-----------------------------+------+-------+-------+--------+-----------+------
oo.3oo.3oo. *b3oo.3oo.&#x & | 1 1 | 20 * ♦ 8 0 | 24 0 | 32 0 0 | 8 8
... ... ... ... .x. | 0 2 | * 40 ♦ 2 6 | 12 12 | 24 4 4 | 8 8
-----------------------------+------+-------+-------+--------+-----------+------
... ... ... ... ox.&#x & | 1 2 | 2 1 | 80 * ♦ 6 0 | 12 0 0 | 4 4
... ... ... .o.3.x. | 0 3 | 0 3 | * 80 ♦ 2 4 | 8 2 2 | 4 4
-----------------------------+------+-------+-------+--------+-----------+------
... ... ... oo.3ox.&#x & ♦ 1 3 | 3 3 | 3 1 | 160 * | 4 0 0 | 2 2
... .o. ... *b3.o.3.x. ♦ 0 4 | 0 6 | 0 4 | * 80 | 2 1 1 | 2 2
-----------------------------+------+-------+-------+--------+-----------+------
... oo. ... *b3oo.3ox.&#x & ♦ 1 4 | 4 6 | 6 4 | 4 1 | 160 * * | 1 1
.o.3.o. ... *b3.o.3.x. ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 16 * | 2 0
... .o.3.o. *b3.o.3.x. ♦ 0 5 | 0 10 | 0 10 | 0 5 | * * 16 | 0 2
-----------------------------+------+-------+-------+--------+-----------+------
oo.3oo. ... *b3oo.3ox.&#x & ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 0 | 32 *
... oo.3oo. *b3oo.3ox.&#x & ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 0 1 | * 32
qo oo3oo3oo *c3oo3ox&#zx → height = 0
(tegum sum of q-line and perp tac)
(tegum product of q-line with tac)
o. o.3o.3o. *c3o.3o. | 2 * ♦ 10 0 | 40 0 | 80 0 | 80 0 0 | 16 16
.o .o3.o3.o *c3.o3.o | * 10 ♦ 2 8 | 16 24 | 48 32 | 64 8 8 | 16 16
------------------------+------+-------+-------+--------+-----------+------
oo oo3oo3oo *c3oo3oo&#x | 1 1 | 20 * ♦ 8 0 | 24 0 | 32 0 0 | 8 8
.. .. .. .. .. .x | 0 2 | * 40 ♦ 2 6 | 12 12 | 24 4 4 | 8 8
------------------------+------+-------+-------+--------+-----------+------
.. .. .. .. .. ox&#x | 1 2 | 2 1 | 80 * ♦ 6 0 | 12 0 0 | 4 4
.. .. .. .. .o3.x | 0 3 | 0 3 | * 80 ♦ 2 4 | 8 2 2 | 4 4
------------------------+------+-------+-------+--------+-----------+------
.. .. .. .. oo3ox&#x ♦ 1 3 | 3 3 | 3 1 | 160 * | 4 0 0 | 2 2
.. .. .o .. *c3.o3.x ♦ 0 4 | 0 6 | 0 4 | * 80 | 2 1 1 | 2 2
------------------------+------+-------+-------+--------+-----------+------
.. .. oo .. *c3oo3ox&#x ♦ 1 4 | 4 6 | 6 4 | 4 1 | 160 * * | 1 1
.. .o3.o .. *c3.o3.x ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 16 * | 2 0
.. .. .o3.o *c3.o3.x ♦ 0 5 | 0 10 | 0 10 | 0 5 | * * 16 | 0 2
------------------------+------+-------+-------+--------+-----------+------
.. oo3oo .. *c3oo3ox&#x ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 0 | 32 *
.. .. oo3oo *c3oo3ox&#x ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 0 1 | * 32
oxoo3oooo3oooo3ooox&#xr → all heights = sqrt(3/5) = 0.774597
(pt || (pseudo pen || pseudo inv pen) || pt)
o(..).3o(..).3o(..).3o(..). & | 2 * ♦ 5 5 0 0 | 10 10 20 0 0 | 10 10 30 30 0 0 0 | 5 5 20 30 20 0 0 0 | 1 1 5 10 10 5
.(o.).3.(o.).3.(o.).3.(o.). & | * 10 ♦ 1 1 4 4 | 4 4 8 6 18 | 6 6 18 18 4 16 12 | 4 4 16 24 16 1 5 10 | 1 1 5 10 10 5
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(o.).3o(o.).3o(o.).3o(o.).&#x & | 1 1 | 10 * * * ♦ 4 0 4 0 0 | 6 0 12 6 0 0 0 | 4 0 12 12 4 0 0 0 | 1 0 4 6 4 1
o(.o).3o(.o).3o(.o).3o(.o).&#x & | 1 1 | * 10 * * ♦ 0 4 4 0 0 | 0 6 6 12 0 0 0 | 0 4 4 12 12 0 0 0 | 0 1 1 4 6 4
.(x.). .(..). .(..). .(..). & | 0 2 | * * 20 * ♦ 1 1 0 3 3 | 3 3 3 3 3 6 3 | 3 3 6 6 6 1 3 4 | 1 1 3 4 4 3
.(oo).3.(oo).3.(oo).3.(oo).&#x | 0 2 | * * * 20 ♦ 0 0 2 0 6 | 0 0 6 6 0 6 6 | 0 0 6 12 6 0 2 6 | 0 0 2 6 6 2
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.). .(..). .(..). .(..).&#x & | 1 2 | 2 0 1 0 | 20 * * * * ♦ 3 0 3 0 0 0 0 | 3 0 6 3 0 0 0 0 | 1 0 3 3 1 0
.(..). .(..). .(..). o(.x).&#x & | 1 2 | 0 2 1 0 | * 20 * * * ♦ 0 3 0 3 0 0 0 | 0 3 0 3 6 0 0 0 | 0 1 0 1 3 3
o(oo).3o(oo).3o(oo).3o(oo).&#x & | 1 2 | 1 1 0 1 | * * 40 * * ♦ 0 0 3 3 0 0 0 | 0 0 3 6 3 0 0 0 | 0 0 1 3 3 1
.(x.).3.(o.). .(..). .(..). & | 0 3 | 0 0 3 0 | * * * 20 * ♦ 1 1 0 0 2 2 0 | 2 2 2 0 2 1 2 1 | 1 1 2 1 1 2
.(xo). .(..). .(..). .(..).&#x & | 0 3 | 0 0 1 2 | * * * * 60 ♦ 0 0 1 1 0 2 2 | 0 0 2 4 2 0 1 3 | 0 0 1 3 3 1
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.).3o(o.). .(..). .(..).&#x & ♦ 1 3 | 3 0 3 0 | 3 0 0 1 0 | 20 * * * * * * | 2 0 2 0 0 0 0 0 | 1 0 2 1 0 0
.(..). .(..). o(.o).3o(.x).&#x & ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 | * 20 * * * * * | 0 2 0 0 2 0 0 0 | 0 1 0 0 1 2
o(xo). .(..). .(..). .(..).&#x & ♦ 1 3 | 2 1 1 2 | 1 0 2 0 1 | * * 60 * * * * | 0 0 2 2 0 0 0 0 | 0 0 1 2 1 0
.(..). .(..). .(..). o(ox).&#x & ♦ 1 3 | 1 2 1 2 | 0 1 2 0 1 | * * * 60 * * * | 0 0 0 2 2 0 0 0 | 0 0 0 1 2 1
.(x.).3.(o.).3.(o.). .(..). & ♦ 0 4 | 0 0 6 0 | 0 0 0 4 0 | * * * * 10 * * | 1 1 0 0 0 1 1 0 | 1 1 1 0 0 1
.(xo).3.(oo). .(..). .(..).&#x & ♦ 0 4 | 0 0 3 3 | 0 0 0 1 3 | * * * * * 40 * | 0 0 1 0 1 0 1 1 | 0 0 1 1 1 1
.(xo). .(..). .(..). .(ox).&#x ♦ 0 4 | 0 0 2 4 | 0 0 0 0 4 | * * * * * * 30 | 0 0 0 2 0 0 0 2 | 0 0 0 2 2 0
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.).3o(o.).3o(o.). .(..).&#x & ♦ 1 4 | 4 0 6 0 | 6 0 0 4 0 | 4 0 0 0 1 0 0 | 10 * * * * * * * | 1 0 1 0 0 0
.(..). o(.o).3o(.o).3o(.x).&#x & ♦ 1 4 | 0 4 6 0 | 0 6 0 4 0 | 0 4 0 0 1 0 0 | * 10 * * * * * * | 0 1 0 0 0 1
o(xo).3o(oo). .(..). .(..).&#x & ♦ 1 4 | 3 1 3 3 | 3 0 3 1 3 | 1 0 3 0 0 1 0 | * * 40 * * * * * | 0 0 1 1 0 0
o(xo). .(..). .(..). o(ox).&#x & ♦ 1 4 | 2 2 2 4 | 1 1 4 0 4 | 0 0 2 2 0 0 1 | * * * 60 * * * * | 0 0 0 1 1 0
.(..). .(..). o(oo).3o(ox).&#x & ♦ 1 4 | 1 3 3 3 | 0 3 3 1 3 | 0 1 0 3 0 1 0 | * * * * 40 * * * | 0 0 0 0 1 1
.(x.).3.(o.).3.(o.).3.(o.). & ♦ 0 5 | 0 0 10 0 | 0 0 0 10 0 | 0 0 0 0 5 0 0 | * * * * * 2 * * | 1 1 0 0 0 0
.(xo).3.(oo).3.(oo). .(..).&#x & ♦ 0 5 | 0 0 6 4 | 0 0 0 4 6 | 0 0 0 0 1 4 0 | * * * * * * 10 * | 0 0 1 0 0 1
.(xo).3.(oo). .(..). .(ox).&#x & ♦ 0 5 | 0 0 4 6 | 0 0 0 1 9 | 0 0 0 0 0 2 3 | * * * * * * * 20 | 0 0 0 1 1 0
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.).3o(o.).3o(o.).3o(o.).&#x & ♦ 1 5 | 5 0 10 0 | 10 0 0 10 0 | 10 0 0 0 5 0 0 | 5 0 0 0 0 1 0 0 | 2 * * * * *
o(.o).3o(.o).3o(.o).3o(.x).&#x & ♦ 1 5 | 0 5 10 0 | 0 10 0 10 0 | 0 10 0 0 5 0 0 | 0 5 0 0 0 1 0 0 | * 2 * * * *
o(xo).3o(oo).3o(oo). .(..).&#x & ♦ 1 5 | 4 1 6 4 | 6 0 4 4 6 | 4 0 6 0 1 4 0 | 1 0 4 0 0 0 1 0 | * * 10 * * *
o(xo).3o(oo). .(..). o(ox).&#x & ♦ 1 5 | 3 2 4 6 | 3 1 6 1 9 | 1 0 6 3 0 2 3 | 0 0 2 3 0 0 0 1 | * * * 20 * *
o(xo). .(..). o(oo).3o(ox).&#x & ♦ 1 5 | 2 3 4 6 | 1 3 6 1 9 | 0 1 3 6 0 2 3 | 0 0 0 3 2 0 0 1 | * * * * 20 *
.(..). o(oo).3o(oo).3o(ox).&#x & ♦ 1 5 | 1 4 6 4 | 0 6 4 4 6 | 0 4 0 6 1 4 0 | 0 1 0 0 4 0 1 0 | * * * * * 10
oqo xoo3ooo3ooo3oox&#xt → both heights = 1/sqrt(10) = 0.316228
(pen || perp pseudo q-line || dual pen)
o.. o..3o..3o..3o.. | 5 * * ♦ 4 2 4 0 0 | 6 8 12 6 8 0 0 | 4 12 12 12 4 24 12 0 0 | 1 8 4 6 4 1 24 24 8 0 0 | 2 8 12 8 2 0
.o. .o.3.o.3.o.3.o. | * 2 * ♦ 0 5 0 5 0 | 0 10 0 0 20 10 0 | 0 10 0 0 0 30 30 10 0 | 0 5 0 0 0 0 20 30 20 5 0 | 1 5 10 10 5 1
..o ..o3..o3..o3..o | * * 5 ♦ 0 0 4 2 4 | 0 0 6 12 8 8 6 | 0 0 4 12 12 12 24 12 4 | 0 0 1 4 6 4 8 24 24 8 1 | 0 2 8 12 8 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x.. ... ... ... | 2 0 0 | 10 * * * * ♦ 3 2 3 0 0 0 0 | 3 6 6 3 0 6 0 0 0 | 1 6 3 3 1 0 12 6 0 0 0 | 2 6 6 2 0 0
oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 10 * * * ♦ 0 4 0 0 4 0 0 | 0 6 0 0 0 12 6 0 0 | 0 4 0 0 0 0 12 12 4 0 0 | 1 4 6 4 1 0
o.o o.o3o.o3o.o3o.o&#x | 1 0 1 | * * 20 * * ♦ 0 0 3 3 2 0 0 | 0 0 3 6 3 6 6 0 0 | 0 0 1 3 3 1 6 12 6 0 0 | 0 2 6 6 2 0
.oo .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * 10 * ♦ 0 0 0 0 4 4 0 | 0 0 0 0 0 6 12 6 0 | 0 0 0 0 0 0 4 12 12 4 0 | 0 1 4 6 4 1
... ... ... ... ..x | 0 0 2 | * * * * 10 ♦ 0 0 0 3 0 2 3 | 0 0 0 3 6 0 6 6 3 | 0 0 0 1 3 3 0 6 12 6 1 | 0 0 2 6 6 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 | 10 * * * * * * ♦ 2 2 2 0 0 0 0 0 0 | 1 4 2 1 0 0 4 0 0 0 0 | 2 4 2 0 0 0
... xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 | * 20 * * * * * ♦ 0 3 0 0 0 3 0 0 0 | 0 3 0 0 0 0 6 3 0 0 0 | 1 3 3 1 0 0
... x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 | * * 30 * * * * ♦ 0 0 3 3 0 2 0 0 0 | 0 0 1 2 1 0 4 4 0 0 0 | 0 2 4 2 0 0
... ... ... ... o.x&#x | 1 0 2 | 0 0 2 0 1 | * * * 30 * * * ♦ 0 0 0 2 2 0 2 0 0 | 0 0 0 1 2 1 0 4 4 0 0 | 0 0 2 4 2 0
ooo ooo3ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 1 0 | * * * * 40 * * ♦ 0 0 0 0 0 3 3 0 0 | 0 0 0 0 0 0 3 6 3 0 0 | 0 1 3 3 1 0
... ... ... ... .ox&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 20 * ♦ 0 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 3 6 3 0 | 0 0 1 3 3 1
... ... ... ..o3..x | 0 0 3 | 0 0 0 0 3 | * * * * * * 10 ♦ 0 0 0 0 2 0 0 2 2 | 0 0 0 0 1 2 0 0 4 4 1 | 0 0 0 2 4 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 | 4 0 0 0 0 0 0 | 5 * * * * * * * * | 1 2 1 0 0 0 0 0 0 0 0 | 2 2 0 0 0 0
... xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 | 1 3 0 0 0 0 0 | * 20 * * * * * * * | 0 2 0 0 0 0 2 0 0 0 0 | 1 2 1 0 0 0
... x.o3o.o ... ...&#x ♦ 3 0 1 | 3 0 3 0 0 | 1 0 3 0 0 0 0 | * * 20 * * * * * * | 0 0 1 1 0 0 2 0 0 0 0 | 0 2 2 0 0 0
... x.o ... ... o.x&#x ♦ 2 0 2 | 1 0 4 0 1 | 0 0 2 2 0 0 0 | * * * 30 * * * * * | 0 0 0 1 1 0 0 2 0 0 0 | 0 0 2 2 0 0
... ... ... o.o3o.x&#x ♦ 1 0 3 | 0 0 3 0 3 | 0 0 0 3 0 0 1 | * * * * 20 * * * * | 0 0 0 0 1 1 0 0 2 0 0 | 0 0 0 2 2 0
... xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 1 0 | 0 1 1 0 2 0 0 | * * * * * 60 * * * | 0 0 0 0 0 0 2 2 0 0 0 | 0 1 2 1 0 0
... ... ... ... oox&#x ♦ 1 1 2 | 0 1 2 2 1 | 0 0 0 1 2 1 0 | * * * * * * 60 * * | 0 0 0 0 0 0 0 2 2 0 0 | 0 0 1 2 1 0
... ... ... .oo3.ox&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 0 3 1 | * * * * * * * 20 * | 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 1 2 1
... ... ..o3..o3..x ♦ 0 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * * 5 | 0 0 0 0 0 1 0 0 0 2 1 | 0 0 0 0 2 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x..3o..3o..3o.. ♦ 5 0 0 | 10 0 0 0 0 | 10 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 2 0 0 0 0 0
... xo.3oo.3oo. ...&#x ♦ 4 1 0 | 6 4 0 0 0 | 4 6 0 0 0 0 0 | 1 4 0 0 0 0 0 0 0 | * 10 * * * * * * * * * | 1 1 0 0 0 0
... x.o3o.o3o.o ...&#x ♦ 4 0 1 | 6 0 4 0 0 | 4 0 6 0 0 0 0 | 1 0 4 0 0 0 0 0 0 | * * 5 * * * * * * * * | 0 2 0 0 0 0
... x.o3o.o ... o.x&#x ♦ 3 0 2 | 3 0 6 0 1 | 1 0 6 3 0 0 0 | 0 0 2 3 0 0 0 0 0 | * * * 10 * * * * * * * | 0 0 2 0 0 0
... x.o ... o.o3o.x&#x ♦ 2 0 3 | 1 0 6 0 3 | 0 0 3 6 0 0 1 | 0 0 0 3 2 0 0 0 0 | * * * * 10 * * * * * * | 0 0 0 2 0 0
... ... o.o3o.o3o.x&#x ♦ 1 0 4 | 0 0 4 0 6 | 0 0 0 6 0 0 4 | 0 0 0 0 4 0 0 0 1 | * * * * * 5 * * * * * | 0 0 0 0 2 0
... xoo3ooo ... ...&#x ♦ 3 1 1 | 3 3 3 1 0 | 1 3 3 0 3 0 0 | 0 1 1 0 0 3 0 0 0 | * * * * * * 40 * * * * | 0 1 1 0 0 0
... xoo ... ... oox&#x ♦ 2 1 2 | 1 2 4 2 1 | 0 1 2 2 4 1 0 | 0 0 0 1 0 2 2 0 0 | * * * * * * * 60 * * * | 0 0 1 1 0 0
... ... ... ooo3oox&#x ♦ 1 1 3 | 0 1 3 3 3 | 0 0 0 3 3 3 1 | 0 0 0 0 1 0 3 1 0 | * * * * * * * * 40 * * | 0 0 0 1 1 0
... ... .oo3.oo3.ox&#x ♦ 0 1 4 | 0 0 0 4 6 | 0 0 0 0 0 6 4 | 0 0 0 0 0 0 0 4 1 | * * * * * * * * * 10 * | 0 0 0 0 1 1
... ..o3..o3..o3..x ♦ 0 0 5 | 0 0 0 0 10 | 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 5 | * * * * * * * * * * 1 | 0 0 0 0 0 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... xo.3oo.3oo.3oo.&#x ♦ 5 1 0 | 10 5 0 0 0 | 10 10 0 0 0 0 0 | 5 10 0 0 0 0 0 0 0 | 1 5 0 0 0 0 0 0 0 0 0 | 2 * * * * *
... xoo3ooo3ooo ...&#x ♦ 4 1 1 | 6 4 4 1 0 | 4 6 6 0 4 0 0 | 1 4 4 0 0 6 0 0 0 | 0 1 1 0 0 0 4 0 0 0 0 | * 10 * * * *
... xoo3ooo ... oox&#x ♦ 3 1 2 | 3 3 6 2 1 | 1 3 6 3 6 1 0 | 0 1 2 3 0 6 3 0 0 | 0 0 0 1 0 0 2 3 0 0 0 | * * 20 * * *
... xoo ... ooo3oox&#x ♦ 2 1 3 | 1 2 6 3 3 | 0 1 3 6 6 3 1 | 0 0 0 3 2 3 6 1 0 | 0 0 0 0 1 0 0 3 2 0 0 | * * * 20 * *
... ... ooo3ooo3oox&#x ♦ 1 1 4 | 0 1 4 4 6 | 0 0 0 6 4 6 4 | 0 0 0 0 4 0 6 4 1 | 0 0 0 0 0 1 0 0 4 1 0 | * * * * 10 *
... .oo3.oo3.oo3.ox&#x ♦ 0 1 5 | 0 0 0 5 10 | 0 0 0 0 0 10 10 | 0 0 0 0 0 0 0 10 5 | 0 0 0 0 0 0 0 0 0 5 1 | * * * * * 2
xox oxo3ooo3ooo4ooo&#xt → both heights = 1/2
(line || pseudo perp hex || line)
o.. o..3o..3o..4o.. & | 4 * ♦ 1 8 1 0 | 8 24 8 0 | 24 32 24 0 | 32 16 32 | 16 16
.o. .o.3.o.3.o.4.o. | * 8 ♦ 0 4 0 6 | 2 24 2 12 | 12 48 12 8 | 24 32 24 | 16 16
--------------------------+-----+-----------+-------------+--------------+----------+------
x.. ... ... ... ... & | 2 0 | 2 * * * ♦ 8 0 0 0 | 24 0 0 0 | 32 0 0 | 16 0
oo. oo.3oo.3oo.4oo.&#x & | 1 1 | * 32 * * ♦ 1 6 1 0 | 6 12 6 0 | 12 8 12 | 8 8
o.o o.o3o.o3o.o4o.o&#x | 2 0 | * * 2 * ♦ 0 0 8 0 | 0 0 24 0 | 0 0 32 | 0 16
... .x. ... ... ... | 0 2 | * * * 24 ♦ 0 4 0 4 | 2 16 2 4 | 8 16 8 | 8 8
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | 16 * * * ♦ 8 0 0 0 | 12 0 0 | 8 0
... ox. ... ... ...&#x & | 1 2 | 0 2 0 1 | * 96 * * ♦ 1 4 1 0 | 4 4 4 | 4 4
ooo ooo3ooo3ooo4ooo&#x | 2 1 | 0 2 1 0 | * * 16 * ♦ 0 0 6 0 | 0 0 12 | 0 8
... .x.3.o. ... ... | 0 3 | 0 0 0 3 | * * * 32 ♦ 0 4 0 2 | 2 8 2 | 4 4
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ox. ... ... ...&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 | 48 * * * | 4 0 0 | 4 0
... ox.3oo. ... ...&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 128 * * | 1 2 1 | 2 2
... oxo ... ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 2 2 0 | * * 48 * | 0 0 4 | 0 4
... .x.3.o.3.o. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * 16 | 0 4 0 | 2 2
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ox.3oo. ... ...&#x & ♦ 2 3 | 1 6 0 3 | 3 6 0 1 | 3 2 0 0 | 64 * * | 2 0
... ox.3oo.3oo. ...&#x & ♦ 1 4 | 0 4 0 6 | 0 6 0 4 | 0 4 0 1 | * 64 * | 1 1
... oxo3ooo ... ...&#x ♦ 2 3 | 0 6 1 3 | 0 6 3 1 | 0 2 3 0 | * * 64 | 0 2
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ox.3oo.3oo. ...&#x & ♦ 2 4 | 1 8 0 6 | 4 12 0 4 | 6 8 0 1 | 4 2 0 | 32 *
... oxo3ooo3ooo ...&#x ♦ 2 4 | 0 8 1 6 | 0 12 4 4 | 0 8 6 1 | 0 2 4 | * 32
ooo3ooo3ooo *b3oxo xox&#xt → both heights = 1/2
(line || pseudo perp hex || line)
o..3o..3o.. *b3o.. o.. & | 4 * ♦ 1 8 1 0 | 24 8 8 0 | 32 24 24 0 0 | 8 8 32 32 | 8 8 8 8
.o.3.o.3.o. *b3.o. .o. | * 8 ♦ 0 4 0 6 | 24 2 2 12 | 48 12 12 4 4 | 16 16 24 24 | 8 8 8 8
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
... ... ... ... x.. & | 2 0 | 2 * * * ♦ 0 8 0 0 | 0 24 0 0 0 | 0 0 32 0 | 8 8 0 0
oo.3oo.3oo. *b3oo. oo.&#x & | 1 1 | * 32 * * ♦ 6 1 1 0 | 12 6 6 0 0 | 4 4 12 12 | 4 4 4 4
o.o3o.o3o.o *b3o.o o.o&#x | 2 0 | * * 2 * ♦ 0 0 8 0 | 0 0 24 0 0 | 0 0 0 32 | 0 0 8 8
... ... ... .x. ... | 0 2 | * * * 24 ♦ 4 0 0 4 | 16 2 2 2 2 | 8 8 8 8 | 4 4 4 4
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
... ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | 96 * * * ♦ 4 1 1 0 0 | 2 2 4 4 | 2 2 2 2
... ... ... ... xo.&#x & | 2 1 | 1 2 0 0 | * 16 * * ♦ 0 6 0 0 0 | 0 0 12 0 | 4 4 0 0
ooo3ooo3ooo *b3ooo ooo&#x | 2 1 | 0 2 1 0 | * * 16 * ♦ 0 0 6 0 0 | 0 0 0 12 | 0 0 4 4
... .o. ... *b3.x. ... | 0 3 | 0 0 0 3 | * * * 32 ♦ 4 0 0 1 1 | 4 4 2 2 | 2 2 2 2
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
... oo. ... *b3ox. ...&#x & ♦ 1 3 | 0 3 0 3 | 3 0 0 1 | 128 * * * * | 1 1 1 1 | 1 1 1 1
... ... ... ox. xo.&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 | * 48 * * * | 0 0 4 0 | 2 2 0 0
... ... ... oxo ...&#x ♦ 2 2 | 0 4 1 1 | 2 0 2 0 | * * 48 * * | 0 0 0 4 | 0 0 2 2
.o.3.o. ... *b3.x. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * 8 * | 4 0 0 0 | 2 0 2 0
... .o.3.o. *b3.x. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * * 8 | 0 4 0 0 | 0 2 0 2
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
oo.3oo. ... *b3ox. ...&#x & ♦ 1 4 | 0 4 0 6 | 6 0 0 4 | 4 0 0 1 0 | 32 * * * | 1 0 1 0
... oo.3oo. *b3ox. ...&#x & ♦ 1 4 | 0 4 0 6 | 6 0 0 4 | 4 0 0 0 1 | * 32 * * | 0 1 0 1
... oo. ... *b3ox. xo.&#x & ♦ 2 3 | 1 6 0 3 | 6 3 0 1 | 2 3 0 0 0 | * * 64 * | 1 1 0 0
... ooo ... *b3oxo ...&#x ♦ 2 3 | 0 6 1 3 | 6 0 3 1 | 2 0 3 0 0 | * * * 64 | 0 0 1 1
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
oo.3oo. ... *b3ox. xo.&#x & ♦ 2 4 | 1 8 0 6 | 12 4 0 4 | 8 6 0 1 0 | 2 0 4 0 | 16 * * *
... oo.3oo. *b3ox. xo.&#x & ♦ 2 4 | 1 8 0 6 | 12 4 0 4 | 8 6 0 0 1 | 0 2 4 0 | * 16 * *
ooo3ooo ... *b3oxo ...&#x ♦ 2 4 | 0 8 1 6 | 12 0 4 4 | 8 0 6 1 0 | 2 0 0 4 | * * 16 *
... ooo3ooo *b3oxo ...&#x ♦ 2 4 | 0 8 1 6 | 12 0 4 4 | 8 0 6 0 1 | 0 2 0 4 | * * * 16
xo4oo ox3oo3oo4oo&#zx → height = 0
(tegum sum of {4} and perp hex)
(tegum product of {4} with hex)
o.4o. o.3o.3o.4o. | 4 * ♦ 2 8 0 | 16 24 0 | 48 32 0 | 64 16 | 32
.o4.o .o3.o3.o4.o | * 8 ♦ 0 4 6 | 4 24 12 | 24 48 8 | 48 32 | 32
---------------------+-----+---------+----------+-----------+--------+---
x. .. .. .. .. .. | 2 0 | 4 * * ♦ 8 0 0 | 24 0 0 | 32 0 | 16
oo4oo oo3oo3oo4oo&#x | 1 1 | * 32 * ♦ 2 6 0 | 12 12 0 | 24 8 | 16
.. .. .x .. .. .. | 0 2 | * * 24 ♦ 0 4 4 | 4 16 4 | 16 16 | 16
---------------------+-----+---------+----------+-----------+--------+---
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | 32 * * ♦ 6 0 0 | 12 0 | 8
.. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * 96 * ♦ 2 4 0 | 8 4 | 8
.. .. .x3.o .. .. | 0 3 | 0 0 3 | * * 32 ♦ 0 4 2 | 4 8 | 8
---------------------+-----+---------+----------+-----------+--------+---
xo .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 96 * * | 4 0 | 4
.. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 | 0 3 1 | * 128 * | 2 2 | 4
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * 16 | 0 4 | 4
---------------------+-----+---------+----------+-----------+--------+---
xo .. ox3oo .. ..&#x ♦ 2 3 | 1 6 3 | 3 6 1 | 3 2 0 | 128 * | 2
.. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 | 0 6 4 | 0 4 1 | * 64 | 2
---------------------+-----+---------+----------+-----------+--------+---
xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2 | 64
xo xo ox3oo3oo *d3oo&#zx → height = 0
(tegum sum of {4} and perp hex)
(tegum product of {4} with hex)
o. o. o.3o.3o. *d3o. | 4 * ♦ 1 1 8 0 | 8 8 24 0 | 24 24 32 0 0 | 32 32 8 8 | 8 8 8 8
.o .o .o3.o3.o *d3.o | * 8 ♦ 0 0 4 6 | 2 2 24 12 | 12 12 48 4 4 | 24 24 16 16 | 8 8 8 8
------------------------+-----+-----------+-------------+---------------+-------------+------------
x. .. .. .. .. .. | 2 0 | 2 * * * ♦ 8 0 0 0 | 24 0 0 0 0 | 32 0 0 0 | 8 8 0 0
.. x. .. .. .. .. | 2 0 | * 2 * * ♦ 0 8 0 0 | 0 24 0 0 0 | 0 32 0 0 | 0 0 8 8
oo oo oo3oo3oo *d3oo&#x | 1 1 | * * 32 * ♦ 1 1 4 0 | 6 6 12 0 0 | 12 12 4 4 | 4 4 4 4
.. .. .x .. .. .. | 0 2 | * * * 24 ♦ 0 0 4 2 | 2 2 16 2 2 | 8 8 8 8 | 4 4 4 4
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. .. .. .. ..&#x | 2 1 | 1 0 2 0 | 16 * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 0
.. xo .. .. .. ..&#x | 2 1 | 0 1 2 0 | * 16 * * ♦ 0 6 0 0 0 | 0 12 0 0 | 0 0 4 4
.. .. ox .. .. ..&#x | 1 2 | 0 0 2 1 | * * 96 * ♦ 1 1 4 0 0 | 4 4 2 2 | 2 2 2 2
.. .. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * 32 ♦ 0 0 4 1 1 | 2 2 4 4 | 2 2 2 2
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. ox .. .. ..&#x ♦ 2 2 | 1 0 4 1 | 2 0 2 0 | 48 * * * * | 4 0 0 0 | 2 2 0 0
.. xo ox .. .. ..&#x ♦ 2 2 | 0 1 4 1 | 0 2 2 0 | * 48 * * * | 0 4 0 0 | 0 0 2 2
.. .. ox3oo .. ..&#x ♦ 1 3 | 0 0 3 3 | 0 0 3 1 | * * 128 * * | 1 1 1 1 | 1 1 1 1
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * 8 * | 0 0 4 0 | 2 0 2 0
.. .. .x3.o .. *d3.o ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * * 8 | 0 0 0 4 | 0 2 0 2
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. ox3oo .. ..&#x ♦ 2 3 | 1 0 6 3 | 3 0 6 1 | 3 0 2 0 0 | 64 * * * | 1 1 0 0
.. xo ox3oo .. ..&#x ♦ 2 3 | 0 1 6 3 | 0 3 6 1 | 0 3 2 0 0 | * 64 * * | 0 0 1 1
.. .. ox3oo3oo ..&#x ♦ 1 4 | 0 0 4 6 | 0 0 6 4 | 0 0 4 1 0 | * * 32 * | 1 0 1 0
.. .. ox3oo .. *d3oo&#x ♦ 1 4 | 0 0 4 6 | 0 0 6 4 | 0 0 4 0 1 | * * * 32 | 0 1 0 1
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 0 8 6 | 4 0 12 4 | 6 0 8 1 0 | 4 0 2 0 | 16 * * *
xo .. ox3oo .. *d3oo&#x ♦ 2 4 | 1 0 8 6 | 4 0 12 4 | 6 0 8 0 1 | 4 0 0 2 | * 16 * *
.. xo ox3oo3oo ..&#x ♦ 2 4 | 0 1 8 6 | 0 4 12 4 | 0 6 8 1 0 | 0 4 2 0 | * * 16 *
.. xo ox3oo .. *d3oo&#x ♦ 2 4 | 0 1 8 6 | 0 4 12 4 | 0 6 8 0 1 | 0 4 0 2 | * * * 16
oxo4ooo xoo3ooo3oox&#xt → both heights = 1/sqrt(8) = 0.353553
(tet || perp pseudo {4} || dual tet)
o.. o.. o..3o..3o.. | 4 * * ♦ 3 4 3 0 0 0 | 3 4 12 6 3 12 0 0 0 | 1 12 12 24 12 3 3 1 12 0 0 0 | 24 12 12 12 4 12 4 0 0 | 12 4 12 4 0
.o. .o. .o.3.o.3.o. | * 4 * ♦ 0 4 0 2 4 0 | 0 8 6 0 0 12 8 6 0 | 0 24 12 12 4 0 0 0 12 12 4 0 | 24 8 24 4 1 6 4 8 1 | 8 2 12 8 2
..o ..o ..o3..o3..o | * * 4 ♦ 0 0 3 0 4 3 | 0 0 0 3 6 12 4 12 3 | 0 12 0 12 0 1 3 3 24 12 12 1 | 12 0 24 4 0 12 12 12 4 | 4 0 12 12 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
... ... x.. ... ... | 2 0 0 | 6 * * * * * ♦ 2 0 4 2 0 0 0 0 0 | 1 0 4 8 8 2 1 0 0 0 0 0 | 8 8 0 8 4 4 0 0 0 | 8 4 4 0 0
oo. oo. oo.3oo.3oo.&#x | 1 1 0 | * 16 * * * * ♦ 0 2 3 0 0 3 0 0 0 | 0 6 6 6 3 0 0 0 3 0 0 0 | 12 6 6 3 1 3 1 0 0 | 6 2 6 2 0
o.o o.o o.o3o.o3o.o&#x | 1 0 1 | * * 12 * * * ♦ 0 0 0 2 2 4 0 0 0 | 0 4 0 8 0 1 2 1 8 0 0 0 | 8 0 8 4 0 4 4 0 0 | 4 0 8 4 0
.x. ... ... ... ... | 0 2 0 | * * * 4 * * ♦ 0 4 0 0 0 0 4 0 0 | 0 12 6 0 0 0 0 0 0 6 0 0 | 12 4 12 0 0 0 0 4 0 | 4 1 6 4 1
.oo .oo .oo3.oo3.oo&#x | 0 1 1 | * * * * 16 * ♦ 0 0 0 0 0 3 2 3 0 | 0 6 0 3 0 0 0 0 6 6 3 0 | 6 0 12 1 0 3 3 6 1 | 2 0 6 6 2
... ... ... ... ..x | 0 0 2 | * * * * * 6 ♦ 0 0 0 0 2 0 0 4 2 | 0 0 0 0 0 0 1 2 8 4 8 1 | 0 0 8 0 0 4 8 8 4 | 0 0 4 8 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
... ... x..3o.. ... | 3 0 0 | 3 0 0 0 0 0 | 4 * * * * * * * * ♦ 1 0 0 0 4 1 0 0 0 0 0 0 | 0 4 0 4 4 0 0 0 0 | 4 4 0 0 0
ox. ... ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 16 * * * * * * * ♦ 0 3 3 0 0 0 0 0 0 0 0 0 | 6 3 3 0 0 0 0 0 0 | 3 1 3 1 0
... ... xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * * 24 * * * * * * ♦ 0 0 2 2 2 0 0 0 0 0 0 0 | 4 4 0 2 1 1 0 0 0 | 4 2 2 0 0
... ... x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 12 * * * * * ♦ 0 0 0 4 0 1 1 0 0 0 0 0 | 4 0 0 4 0 4 0 0 0 | 4 0 4 0 0
... ... ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 12 * * * * ♦ 0 0 0 0 0 0 1 1 4 0 0 0 | 0 0 4 0 0 4 4 0 0 | 0 0 4 4 0
ooo ooo ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 48 * * * ♦ 0 2 0 2 0 0 0 0 2 0 0 0 | 4 0 4 1 0 2 1 0 0 | 2 0 4 2 0
.xo ... ... ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * 16 * * ♦ 0 3 0 0 0 0 0 0 0 3 0 0 | 3 0 6 0 0 0 0 3 0 | 1 0 3 3 1
... ... ... ... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * 24 * ♦ 0 0 0 0 0 0 0 0 2 2 2 0 | 0 0 4 0 0 1 4 4 1 | 0 0 2 4 2
... ... ... ..o3..x | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 4 ♦ 0 0 0 0 0 0 0 1 0 0 4 1 | 0 0 0 0 0 0 4 4 4 | 0 0 0 4 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
... ... x..3o..3o.. ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * | 0 0 0 0 4 0 0 0 0 | 0 4 0 0 0
oxo ... ... ... ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 1 0 0 0 2 1 0 0 | * 48 * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 | 1 0 2 1 0
ox. ... xo. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 0 0 | * * 24 * * * * * * * * * | 2 2 0 0 0 0 0 0 0 | 2 1 1 0 0
... ... xoo ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 0 1 1 0 2 0 0 0 | * * * 48 * * * * * * * * | 2 0 0 1 0 1 0 0 0 | 2 0 2 0 0
... ... xo.3oo. ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 0 3 0 0 0 0 0 0 | * * * * 16 * * * * * * * | 0 2 0 1 1 0 0 0 0 | 2 2 0 0 0
... ... x.o3o.o ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 | 1 0 0 3 0 0 0 0 0 | * * * * * 4 * * * * * * | 0 0 0 4 0 0 0 0 0 | 4 0 0 0 0
... ... x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 0 2 2 0 0 0 0 | * * * * * * 6 * * * * * | 0 0 0 0 0 4 0 0 0 | 0 0 4 0 0
... ... ... o.o3o.x&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 0 3 0 0 0 1 | * * * * * * * 4 * * * * | 0 0 0 0 0 0 4 0 0 | 0 0 0 4 0
... ... ... ... oox&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 0 1 2 0 1 0 | * * * * * * * * 48 * * * | 0 0 2 0 0 1 1 0 0 | 0 0 2 2 0
.xo ... ... ... .ox&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * * 24 * * | 0 0 2 0 0 0 0 2 0 | 0 0 1 2 1
... ... ... .oo3.ox&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * 16 * | 0 0 0 2 0 0 1 2 1 | 0 0 0 2 2
... ... ..o3..o3..x ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * 1 | 0 0 0 2 0 0 0 0 4 | 0 0 0 0 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
oxo ... xoo ... ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 0 2 2 1 0 4 1 0 0 | 0 2 1 2 0 0 0 0 0 0 0 0 | 48 * * * * * * * * | 1 0 1 0 0
ox. ... xo.3oo. ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 3 6 0 0 0 0 0 0 | 0 0 3 0 2 0 0 0 0 0 0 0 | * 16 * * * * * * * | 1 1 0 0 0
oxo ... ... ... oox&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 1 0 0 1 4 2 2 0 | 0 2 0 0 0 0 0 0 2 1 0 0 | * * 48 * * * * * * | 0 0 1 1 0
... ... xoo3ooo ...&#x ♦ 3 1 1 | 3 3 3 0 1 0 | 1 0 3 3 0 3 0 0 0 | 0 0 0 3 1 1 0 0 0 0 0 0 | * * * 16 * * * * * | 2 0 0 0 0
... ... xo.3oo.3oo.&#x ♦ 4 1 0 | 6 4 0 0 0 0 | 4 0 6 0 0 0 0 0 0 | 1 0 0 0 4 0 0 0 0 0 0 0 | * * * * 4 * * * * | 0 2 0 0 0
... ... xoo ... oox&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 0 0 1 2 2 4 0 1 0 | 0 0 0 2 0 0 1 0 2 0 0 0 | * * * * * 24 * * * | 0 0 2 0 0
... ... ... ooo3oox&#x ♦ 1 1 3 | 0 1 3 0 3 3 | 0 0 0 0 3 3 0 3 1 | 0 0 0 0 0 0 0 1 3 0 1 0 | * * * * * * 16 * * | 0 0 0 2 0
.xo ... ... .oo3.ox&#x ♦ 0 2 3 | 0 0 0 1 6 3 | 0 0 0 0 0 0 3 6 1 | 0 0 0 0 0 0 0 0 0 3 2 0 | * * * * * * * 16 * | 0 0 0 1 1
... ... .oo3.oo3.ox&#x ♦ 0 1 4 | 0 0 0 0 4 6 | 0 0 0 0 0 0 0 6 4 | 0 0 0 0 0 0 0 0 0 0 4 1 | * * * * * * * * 4 | 0 0 0 0 2
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
oxo ... xoo3ooo ...&#x ♦ 3 2 1 | 3 6 3 1 2 0 | 1 3 6 3 0 6 1 0 0 | 0 3 3 6 2 1 0 0 0 0 0 0 | 3 1 0 2 0 0 0 0 0 | 16 * * * *
ox. ... xo.3oo.3oo.&#x ♦ 4 2 0 | 6 8 0 1 0 0 | 4 4 12 0 0 0 0 0 0 | 1 0 6 0 8 0 0 0 0 0 0 0 | 0 4 0 0 2 0 0 0 0 | * 4 * * *
oxo ... xoo ... oox&#x ♦ 2 2 2 | 1 4 4 1 4 1 | 0 2 2 2 2 8 2 2 0 | 0 4 1 4 0 0 1 0 4 1 0 0 | 2 0 2 0 0 2 0 0 0 | * * 24 * *
oxo ... ... ooo3oox&#x ♦ 1 2 3 | 0 2 3 1 6 3 | 0 1 0 0 3 6 3 6 1 | 0 3 0 0 0 0 0 1 6 3 2 0 | 0 0 3 0 0 0 2 1 0 | * * * 16 *
.xo ... .oo3.oo3.ox&#x ♦ 0 2 4 | 0 0 0 1 8 6 | 0 0 0 0 0 0 4 12 4 | 0 0 0 0 0 0 0 0 0 6 8 1 | 0 0 0 0 0 0 0 4 2 | * * * * 4
oxo oxo xoo3ooo3oox&#xt → both heights = 1/sqrt(8) = 0.353553
(tet || perp pseudo {4} || dual tet)
o.. o.. o..3o..3o.. | 4 * * ♦ 3 4 3 0 0 0 0 | 3 2 2 12 6 3 12 0 0 0 0 | 1 6 6 6 6 24 12 3 3 1 12 0 0 0 0 | 12 6 6 12 6 6 12 4 12 4 0 0 0 | 6 2 6 2 6 2 6 2 0 0
.o. .o. .o.3.o.3.o. | * 4 * ♦ 0 4 0 1 1 4 0 | 0 4 4 6 0 0 12 4 4 6 0 | 0 12 6 12 6 12 4 0 0 0 12 6 6 4 0 | 12 4 12 12 4 12 4 1 6 4 4 4 1 | 4 1 6 4 4 1 6 4 1 1
..o ..o ..o3..o3..o | * * 4 ♦ 0 0 3 0 0 4 3 | 0 0 0 0 3 6 12 2 2 12 3 | 0 6 0 6 0 12 0 1 3 3 24 6 6 12 1 | 6 0 12 6 0 12 4 0 12 12 6 6 4 | 2 0 6 6 2 0 6 6 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
... ... x.. ... ... | 2 0 0 | 6 * * * * * * ♦ 2 0 0 4 2 0 0 0 0 0 0 | 1 0 2 0 2 8 8 2 1 0 0 0 0 0 0 | 4 4 0 4 4 0 8 4 4 0 0 0 0 | 4 2 2 0 4 2 2 0 0 0
oo. oo. oo.3oo.3oo.&#x | 1 1 0 | * 16 * * * * * ♦ 0 1 1 3 0 0 3 0 0 0 0 | 0 3 3 3 3 6 3 0 0 0 3 0 0 0 0 | 6 3 3 6 3 3 3 1 3 1 0 0 0 | 3 1 3 1 3 1 3 1 0 0
o.o o.o o.o3o.o3o.o&#x | 1 0 1 | * * 12 * * * * ♦ 0 0 0 0 2 2 4 0 0 0 0 | 0 2 0 2 0 8 0 1 2 1 8 0 0 0 0 | 4 0 4 4 0 4 4 0 4 4 0 0 0 | 2 0 4 2 2 0 4 2 0 0
.x. ... ... ... ... | 0 2 0 | * * * 2 * * * ♦ 0 4 0 0 0 0 0 4 0 0 0 | 0 12 6 0 0 0 0 0 0 0 0 6 0 0 0 | 12 4 12 0 0 0 0 0 0 0 4 0 0 | 4 1 6 4 0 0 0 0 1 0
... .x. ... ... ... | 0 2 0 | * * * * 2 * * ♦ 0 0 4 0 0 0 0 0 4 0 0 | 0 0 0 12 6 0 0 0 0 0 0 0 6 0 0 | 0 0 0 12 4 12 0 0 0 0 0 4 0 | 0 0 0 0 4 1 6 4 0 1
.oo .oo .oo3.oo3.oo&#x | 0 1 1 | * * * * * 16 * ♦ 0 0 0 0 0 0 3 1 1 3 0 | 0 3 0 3 0 3 0 0 0 0 6 3 3 3 0 | 3 0 6 3 0 6 1 0 3 3 3 3 1 | 1 0 3 3 1 0 3 3 1 1
... ... ... ... ..x | 0 0 2 | * * * * * * 6 ♦ 0 0 0 0 0 2 0 0 0 4 2 | 0 0 0 0 0 0 0 0 1 2 8 2 2 8 1 | 0 0 4 0 0 4 0 0 4 8 4 4 4 | 0 0 2 4 0 0 2 4 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
... ... x..3o.. ... | 3 0 0 | 3 0 0 0 0 0 0 | 4 * * * * * * * * * * ♦ 1 0 0 0 0 0 4 1 0 0 0 0 0 0 0 | 0 2 0 0 2 0 4 4 0 0 0 0 0 | 2 2 0 0 2 2 0 0 0 0
ox. ... ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 0 | * 8 * * * * * * * * * ♦ 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 | 6 3 3 0 0 0 0 0 0 0 0 0 0 | 3 1 3 1 0 0 0 0 0 0
... ox. ... ... ...&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 8 * * * * * * * * ♦ 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 | 0 0 0 6 3 3 0 0 0 0 0 0 0 | 0 0 0 0 3 1 3 1 0 0
... ... xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 0 0 | * * * 24 * * * * * * * ♦ 0 0 1 0 1 2 2 0 0 0 0 0 0 0 0 | 2 2 0 2 2 0 2 1 1 0 0 0 0 | 2 1 1 0 2 1 1 0 0 0
... ... x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * * * 12 * * * * * * ♦ 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 | 2 0 0 2 0 0 4 0 4 0 0 0 0 | 2 0 2 0 2 0 2 0 0 0
... ... ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * * 12 * * * * * ♦ 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 | 0 0 2 0 0 2 0 0 4 4 0 0 0 | 0 0 2 2 0 0 2 2 0 0
ooo ooo ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * * * 48 * * * * ♦ 0 1 0 1 0 2 0 0 0 0 2 0 0 0 0 | 2 0 2 2 0 2 1 0 2 1 0 0 0 | 1 0 2 1 1 0 2 1 0 0
.xo ... ... ... ...&#x | 0 2 1 | 0 0 0 1 0 2 0 | * * * * * * * 8 * * * ♦ 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 | 3 0 6 0 0 0 0 0 0 0 3 0 0 | 1 0 3 3 0 0 0 0 1 0
... .xo ... ... ...&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * * 8 * * ♦ 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 | 0 0 0 3 0 6 0 0 0 0 0 3 0 | 0 0 0 0 1 0 3 3 0 1
... ... ... ... .ox&#x | 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * * * * 24 * ♦ 0 0 0 0 0 0 0 0 0 0 2 1 1 2 0 | 0 0 2 0 0 2 0 0 1 4 2 2 1 | 0 0 1 2 0 0 1 2 1 1
... ... ... ..o3..x | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * 4 ♦ 0 0 0 0 0 0 0 0 0 1 0 0 0 4 1 | 0 0 0 0 0 0 0 0 0 4 2 2 4 | 0 0 0 2 0 0 0 2 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
... ... x..3o..3o.. ♦ 4 0 0 | 6 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 4 0 0 0 0 0 | 0 2 0 0 0 2 0 0 0 0
oxo ... ... ... ...&#x ♦ 1 2 1 | 0 2 1 1 0 2 0 | 0 1 0 0 0 0 2 1 0 0 0 | * 24 * * * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0 0 0
ox. ... xo. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 0 | 0 2 0 2 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 0 | 2 1 1 0 0 0 0 0 0 0
... oxo ... ... ...&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 | 0 0 1 0 0 0 2 0 1 0 0 | * * * 24 * * * * * * * * * * * | 0 0 0 2 0 2 0 0 0 0 0 0 0 | 0 0 0 0 1 0 2 1 0 0
... ox. xo. ... ...&#x ♦ 2 2 0 | 1 4 0 0 1 0 0 | 0 0 2 2 0 0 0 0 0 0 0 | * * * * 12 * * * * * * * * * * | 0 0 0 2 2 0 0 0 0 0 0 0 0 | 0 0 0 0 2 1 1 0 0 0
... ... xoo ... ...&#x ♦ 2 1 1 | 1 2 2 0 0 1 0 | 0 0 0 1 1 0 2 0 0 0 0 | * * * * * 48 * * * * * * * * * | 1 0 0 1 0 0 1 0 1 0 0 0 0 | 1 0 1 0 1 0 1 0 0 0
... ... xo.3oo. ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * * * * * * 16 * * * * * * * * | 0 1 0 0 1 0 1 1 0 0 0 0 0 | 1 1 0 0 1 1 0 0 0 0
... ... x.o3o.o ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 0 | 1 0 0 0 3 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * | 0 0 0 0 0 0 4 0 0 0 0 0 0 | 2 0 0 0 2 0 0 0 0 0
... ... x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 0 1 | 0 0 0 0 2 2 0 0 0 0 0 | * * * * * * * * 6 * * * * * * | 0 0 0 0 0 0 0 0 4 0 0 0 0 | 0 0 2 0 0 0 2 0 0 0
... ... ... o.o3o.x&#x ♦ 1 0 3 | 0 0 3 0 0 0 3 | 0 0 0 0 0 3 0 0 0 0 1 | * * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 0 0 4 0 0 0 | 0 0 0 2 0 0 0 2 0 0
... ... ... ... oox&#x ♦ 1 1 2 | 0 1 2 0 0 2 1 | 0 0 0 0 0 1 2 0 0 1 0 | * * * * * * * * * * 48 * * * * | 0 0 1 0 0 1 0 0 1 1 0 0 0 | 0 0 1 1 0 0 1 1 0 0
.xo ... ... ... .ox&#x ♦ 0 2 2 | 0 0 0 1 0 4 1 | 0 0 0 0 0 0 0 2 0 2 0 | * * * * * * * * * * * 12 * * * | 0 0 2 0 0 0 0 0 0 0 2 0 0 | 0 0 1 2 0 0 0 0 1 0
... .xo ... ... .ox&#x ♦ 0 2 2 | 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * 12 * * | 0 0 0 0 0 2 0 0 0 0 0 2 0 | 0 0 0 0 0 0 1 2 0 1
... ... ... .oo3.ox&#x ♦ 0 1 3 | 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * * * 16 * | 0 0 0 0 0 0 2 0 0 1 1 1 1 | 0 0 0 1 0 0 0 1 1 1
... ... ..o3..o3..x ♦ 0 0 4 | 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 2 0 0 0 0 0 4 | 0 0 0 0 0 0 0 0 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
oxo ... xoo ... ...&#x ♦ 2 2 1 | 1 4 2 1 0 2 0 | 0 2 0 2 1 0 4 1 0 0 0 | 0 2 1 0 0 2 0 0 0 0 0 0 0 0 0 | 24 * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0
ox. ... xo.3oo. ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 0 | 1 3 0 6 0 0 0 0 0 0 0 | 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0
oxo ... ... ... oox&#x ♦ 1 2 2 | 0 2 2 1 0 4 1 | 0 1 0 0 0 1 4 2 0 2 0 | 0 2 0 0 0 0 0 0 0 0 2 1 0 0 0 | * * 24 * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0
... oxo xoo ... ...&#x ♦ 2 2 1 | 1 4 2 0 1 2 0 | 0 0 2 2 1 0 4 0 1 0 0 | 0 0 0 2 1 2 0 0 0 0 0 0 0 0 0 | * * * 24 * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0
... ox. xo.3oo. ...&#x ♦ 3 2 0 | 3 6 0 0 1 0 0 | 1 0 3 6 0 0 0 0 0 0 0 | 0 0 0 0 3 0 2 0 0 0 0 0 0 0 0 | * * * * 8 * * * * * * * * | 0 0 0 0 1 1 0 0 0 0
... oxo ... ... oox&#x ♦ 1 2 2 | 0 2 2 0 1 4 1 | 0 0 1 0 0 1 4 0 2 2 0 | 0 0 0 2 0 0 0 0 0 0 2 0 1 0 0 | * * * * * 24 * * * * * * * | 0 0 0 0 0 0 1 1 0 0
... ... xoo3ooo ...&#x ♦ 3 1 1 | 3 3 3 0 0 1 0 | 1 0 0 3 3 0 3 0 0 0 0 | 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 | * * * * * * 16 * * * * * * | 1 0 0 0 1 0 0 0 0 0
... ... xo.3oo.3oo.&#x ♦ 4 1 0 | 6 4 0 0 0 0 0 | 4 0 0 6 0 0 0 0 0 0 0 | 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * | 0 1 0 0 0 1 0 0 0 0
... ... xoo ... oox&#x ♦ 2 1 2 | 1 2 4 0 0 2 1 | 0 0 0 1 2 2 4 0 0 1 0 | 0 0 0 0 0 2 0 0 1 0 2 0 0 0 0 | * * * * * * * * 24 * * * * | 0 0 1 0 0 0 1 0 0 0
... ... ... ooo3oox&#x ♦ 1 1 3 | 0 1 3 0 0 3 3 | 0 0 0 0 0 3 3 0 0 3 1 | 0 0 0 0 0 0 0 0 0 1 3 0 0 1 0 | * * * * * * * * * 16 * * * | 0 0 0 1 0 0 0 1 0 0
.xo ... ... .oo3.ox&#x ♦ 0 2 3 | 0 0 0 1 0 6 3 | 0 0 0 0 0 0 0 3 0 6 1 | 0 0 0 0 0 0 0 0 0 0 0 3 0 2 0 | * * * * * * * * * * 8 * * | 0 0 0 1 0 0 0 0 1 0
... .xo ... .oo3.ox&#x ♦ 0 2 3 | 0 0 0 0 1 6 3 | 0 0 0 0 0 0 0 0 3 6 1 | 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 | * * * * * * * * * * * 8 * | 0 0 0 0 0 0 0 1 0 1
... ... .oo3.oo3.ox&#x ♦ 0 1 4 | 0 0 0 0 0 4 6 | 0 0 0 0 0 0 0 0 0 6 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 | * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 1
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
oxo ... xoo3ooo ...&#x ♦ 3 2 1 | 3 6 3 1 0 2 0 | 1 3 0 6 3 0 6 1 0 0 0 | 0 3 3 0 0 6 2 1 0 0 0 0 0 0 0 | 3 1 0 0 0 0 2 0 0 0 0 0 0 | 8 * * * * * * * * *
ox. ... xo.3oo.3oo.&#x ♦ 4 2 0 | 6 8 0 1 0 0 0 | 4 4 0 12 0 0 0 0 0 0 0 | 1 0 6 0 0 0 8 0 0 0 0 0 0 0 0 | 0 4 0 0 0 0 0 2 0 0 0 0 0 | * 2 * * * * * * * *
oxo ... xoo ... oox&#x ♦ 2 2 2 | 1 4 4 1 0 4 1 | 0 2 0 2 2 2 8 2 0 2 0 | 0 4 1 0 0 4 0 0 1 0 4 1 0 0 0 | 2 0 2 0 0 0 0 0 2 0 0 0 0 | * * 12 * * * * * * *
oxo ... ... ooo3oox&#x ♦ 1 2 3 | 0 2 3 1 0 6 3 | 0 1 0 0 0 3 6 3 0 6 1 | 0 3 0 0 0 0 0 0 0 1 6 3 0 2 0 | 0 0 3 0 0 0 0 0 0 2 1 0 0 | * * * 8 * * * * * *
... oxo xoo3ooo ...&#x ♦ 3 2 1 | 3 6 3 0 1 2 0 | 1 0 3 6 3 0 6 0 1 0 0 | 0 0 0 3 3 6 2 1 0 0 0 0 0 0 0 | 0 0 0 3 1 0 2 0 0 0 0 0 0 | * * * * 8 * * * * *
... ox. xo.3oo.3oo.&#x ♦ 4 2 0 | 6 8 0 0 1 0 0 | 4 0 4 12 0 0 0 0 0 0 0 | 1 0 0 0 6 0 8 0 0 0 0 0 0 0 0 | 0 0 0 0 4 0 0 2 0 0 0 0 0 | * * * * * 2 * * * *
... oxo xoo ... oox&#x ♦ 2 2 2 | 1 4 4 0 1 4 1 | 0 0 2 2 2 2 8 0 2 2 0 | 0 0 0 4 1 4 0 0 1 0 4 0 1 0 0 | 0 0 0 2 0 2 0 0 2 0 0 0 0 | * * * * * * 12 * * *
... oxo ... ooo3oox&#x ♦ 1 2 3 | 0 2 3 0 1 6 3 | 0 0 1 0 0 3 6 0 3 6 1 | 0 0 0 3 0 0 0 0 0 1 6 0 3 2 0 | 0 0 0 0 0 3 0 0 0 2 0 1 0 | * * * * * * * 8 * *
.xo ... .oo3.oo3.ox&#x ♦ 0 2 4 | 0 0 0 1 0 8 6 | 0 0 0 0 0 0 0 4 0 12 4 | 0 0 0 0 0 0 0 0 0 0 0 6 0 8 1 | 0 0 0 0 0 0 0 0 0 0 4 0 2 | * * * * * * * * 2 *
... .xo .oo3.oo3.ox&#x ♦ 0 2 4 | 0 0 0 0 1 8 6 | 0 0 0 0 0 0 0 0 4 12 4 | 0 0 0 0 0 0 0 0 0 0 0 0 6 8 1 | 0 0 0 0 0 0 0 0 0 0 0 4 2 | * * * * * * * * * 2
xoxo oxoo3oooo3ooox&#xr → height(1,2) = height(1,4) = height(2,3) = height(3,4) = sqrt(5/8) = 0.790569
height(1,3) = 1
height(2,4) = 1/sqrt(2) = 0.707107
o... o...3o...3o... & | 4 * ♦ 1 8 1 0 0 | 8 12 8 12 0 0 | 12 8 12 12 24 12 0 0 0 | 8 2 8 24 8 6 24 | 2 2 8 6 8 6
.o.. .o..3.o..3.o.. & | * 8 ♦ 0 4 0 3 3 | 2 12 2 12 3 9 | 6 12 8 8 36 6 1 4 3 | 6 4 6 18 16 12 18 | 2 2 8 6 8 6
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
x... .... .... .... & | 2 0 | 2 * * * * ♦ 8 0 0 0 0 0 | 12 0 0 12 0 0 0 0 0 | 8 0 0 8 0 0 0 | 2 0 8 6 0 0
oo.. oo..3oo..3oo..&#x & | 1 1 | * 32 * * * ♦ 1 3 1 3 0 0 | 3 3 3 3 9 3 0 0 0 | 3 1 3 9 4 3 9 | 1 1 4 3 4 3
o.o. o.o.3o.o.3o.o.&#x | 2 0 | * * 2 * * ♦ 0 0 8 0 0 0 | 0 0 12 0 0 12 0 0 0 | 0 0 8 0 0 0 24 | 0 2 0 0 8 6
.... .x.. .... .... & | 0 2 | * * * 12 * ♦ 0 4 0 0 2 2 | 2 8 2 0 8 0 1 2 1 | 4 4 4 4 8 4 4 | 2 2 4 2 4 2
.o.o .o.o3.o.o3.o.o&#x | 0 2 | * * * * 12 ♦ 0 0 0 4 0 4 | 0 0 0 2 16 2 0 2 2 | 0 0 0 8 8 8 8 | 0 0 4 4 4 4
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. .... .... ....&#x & | 2 1 | 1 2 0 0 0 | 16 * * * * * ♦ 3 0 0 3 0 0 0 0 0 | 3 0 0 9 0 0 0 | 1 0 4 3 0 0
.... ox.. .... ....&#x & | 1 2 | 0 2 0 1 0 | * 48 * * * * ♦ 1 2 1 0 2 0 0 0 0 | 2 1 2 2 2 1 2 | 1 1 2 1 2 1
ooo. ooo.3ooo.3ooo.&#x & | 2 1 | 0 2 1 0 0 | * * 16 * * * ♦ 0 0 3 0 0 3 0 0 0 | 0 0 3 0 0 0 9 | 0 1 0 0 4 3
oo.o oo.o3oo.o3oo.o&#x & | 1 2 | 0 2 0 0 1 | * * * 48 * * ♦ 0 0 0 1 4 1 0 0 0 | 0 0 0 4 2 2 4 | 0 0 2 2 2 2
.... .x..3.o.. .... & | 0 3 | 0 0 0 3 0 | * * * * 8 * ♦ 0 4 0 0 0 0 1 1 0 | 2 4 2 0 4 0 0 | 2 2 2 0 2 0
.... .x.o .... ....&#x & | 0 3 | 0 0 0 1 2 | * * * * * 24 ♦ 0 0 0 0 4 0 0 1 1 | 0 0 0 2 4 4 2 | 0 0 2 2 2 2
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. ox.. .... ....&#x & ♦ 2 2 | 1 4 0 1 0 | 2 2 0 0 0 0 | 24 * * * * * * * * | 2 0 0 2 0 0 0 | 1 0 2 1 0 0
.... ox..3oo.. ....&#x & ♦ 1 3 | 0 3 0 3 0 | 0 3 0 0 1 0 | * 32 * * * * * * * | 1 1 1 0 1 0 0 | 1 1 1 0 1 0
.... oxo. .... ....&#x & ♦ 2 2 | 0 4 1 1 0 | 0 2 2 0 0 0 | * * 24 * * * * * * | 0 0 2 0 0 0 2 | 0 1 0 0 2 1
xo.o .... .... ....&#x & ♦ 2 2 | 1 4 0 0 1 | 2 0 0 2 0 0 | * * * 24 * * * * * | 0 0 0 4 0 0 0 | 0 0 2 2 0 0
.... ox.o .... ....&#x & ♦ 1 3 | 0 3 0 1 2 | 0 1 0 2 0 1 | * * * * 96 * * * * | 0 0 0 1 1 1 1 | 0 0 1 1 1 1
oooo oooo3oooo3oooo&#x ♦ 2 2 | 0 4 1 0 1 | 0 0 2 2 0 0 | * * * * * 24 * * * | 0 0 0 0 0 0 4 | 0 0 0 0 2 2
.... .x..3.o..3.o.. & ♦ 0 4 | 0 0 0 6 0 | 0 0 0 0 4 0 | * * * * * * 2 * * | 0 4 0 0 0 0 0 | 2 2 0 0 0 0
.... .x.o3.o.o ....&#x & ♦ 0 4 | 0 0 0 3 3 | 0 0 0 0 1 3 | * * * * * * * 8 * | 0 0 0 0 4 0 0 | 0 0 2 0 2 0
.... .x.o .... .o.x&#x ♦ 0 4 | 0 0 0 2 4 | 0 0 0 0 0 4 | * * * * * * * * 6 | 0 0 0 0 0 4 0 | 0 0 0 2 0 2
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. ox..3oo.. ....&#x & ♦ 2 3 | 1 6 0 3 0 | 3 6 0 0 1 0 | 3 2 0 0 0 0 0 0 0 | 16 * * * * * * | 1 0 1 0 0 0
.... ox..3oo..3oo..&#x & ♦ 1 4 | 0 4 0 6 0 | 0 6 0 0 4 0 | 0 4 0 0 0 0 1 0 0 | * 8 * * * * * | 1 1 0 0 0 0
.... oxo.3ooo. ....&#x & ♦ 2 3 | 0 6 1 3 0 | 0 6 3 0 1 0 | 0 2 3 0 0 0 0 0 0 | * * 16 * * * * | 0 1 0 0 1 0
xo.o ox.o .... ....&#x & ♦ 2 3 | 1 6 0 1 2 | 3 2 0 4 0 1 | 1 0 0 2 2 0 0 0 0 | * * * 48 * * * | 0 0 1 1 0 0
.... ox.o3oo.o ....&#x & ♦ 1 4 | 0 4 0 3 3 | 0 3 0 3 1 3 | 0 1 0 0 3 0 0 1 0 | * * * * 32 * * | 0 0 1 0 1 0
.... ox.o .... oo.x&#x & ♦ 1 4 | 0 4 0 2 4 | 0 2 0 4 0 4 | 0 0 0 0 4 0 0 0 1 | * * * * * 24 * | 0 0 0 1 0 1
.... oxoo .... ....&#x & ♦ 2 3 | 0 6 1 1 2 | 0 2 3 4 0 1 | 0 0 1 0 2 2 0 0 0 | * * * * * * 48 | 0 0 0 0 1 1
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. ox..3oo..3oo..&#x & ♦ 2 4 | 1 8 0 6 0 | 4 12 0 0 4 0 | 6 8 0 0 0 0 1 0 0 | 4 2 0 0 0 0 0 | 4 * * * * *
.... oxo.3ooo.3ooo.&#x & ♦ 2 4 | 0 8 1 6 0 | 0 12 4 0 4 0 | 0 8 6 0 0 0 1 0 0 | 0 2 4 0 0 0 0 | * 4 * * * *
xo.o ox.o3oo.o ....&#x & ♦ 2 4 | 1 8 0 3 3 | 4 6 0 6 1 3 | 3 2 0 3 6 0 0 1 0 | 1 0 0 3 2 0 0 | * * 16 * * *
xo.o ox.o .... oo.x&#x & ♦ 2 4 | 1 8 0 2 4 | 4 4 0 8 0 4 | 2 0 0 4 8 0 0 0 1 | 0 0 0 4 0 2 0 | * * * 12 * *
.... oxoo3oooo ....&#x & ♦ 2 4 | 0 8 1 3 3 | 0 6 4 6 1 3 | 0 2 3 0 6 3 0 1 0 | 0 0 1 0 2 0 3 | * * * * 16 *
.... oxoo .... ooox&#x ♦ 2 4 | 0 8 1 2 4 | 0 4 4 8 0 4 | 0 0 2 0 8 4 0 0 1 | 0 0 0 0 0 2 4 | * * * * * 12
xoo3oox oxo3ooo4ooo&#xt → both heights = 1/sqrt(6) = 0.408248
({3} || pseudo perp oct || dual {3})
o..3o.. o..3o..4o.. & | 6 * ♦ 2 6 2 0 | 1 12 12 3 12 0 | 6 24 8 18 24 | 12 16 36 16 | 8 24
.o.3.o. .o.3.o.4.o. | * 6 ♦ 0 6 0 4 | 0 6 24 0 6 4 | 2 24 24 6 24 | 8 24 24 24 | 8 24
--------------------------+-----+-----------+----------------+----------------+-------------+------
x.. ... ... ... ... & | 2 0 | 6 * * * ♦ 1 6 0 1 0 0 | 6 12 0 6 0 | 12 8 12 0 | 8 8
oo.3oo. oo.3oo.4oo.&#x & | 1 1 | * 36 * * ♦ 0 2 4 0 2 0 | 1 8 4 3 8 | 4 8 12 8 | 4 12
o.o3o.o o.o3o.o4o.o&#x | 2 0 | * * 6 * ♦ 0 0 0 2 6 0 | 0 0 0 12 12 | 0 0 24 8 | 0 16
... ... .x. ... ... | 0 2 | * * * 12 ♦ 0 0 6 0 0 2 | 0 6 12 0 6 | 2 12 6 12 | 4 12
--------------------------+-----+-----------+----------------+----------------+-------------+------
x..3o.. ... ... ... & | 3 0 | 3 0 0 0 | 2 * * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 8 0
xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | * 36 * * * * ♦ 1 4 0 1 0 | 4 4 4 0 | 4 4
... ... ox. ... ...&#x & | 1 2 | 0 2 0 1 | * * 72 * * * ♦ 0 2 2 0 2 | 1 4 3 4 | 2 6
x.o ... ... ... ...&#x & | 3 0 | 1 0 2 0 | * * * 6 * * ♦ 0 0 0 6 0 | 0 0 12 0 | 0 8
ooo3ooo ooo3ooo4ooo&#x | 2 1 | 0 2 1 0 | * * * * 36 * ♦ 0 0 0 2 4 | 0 0 8 4 | 0 8
... ... .x.3.o. ... | 0 3 | 0 0 0 3 | * * * * * 8 ♦ 0 0 6 0 0 | 0 6 0 6 | 2 6
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 | 12 * * * * | 4 0 0 0 | 4 0
xo. ... ox. ... ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 | * 72 * * * | 1 2 1 0 | 2 2
... ... ox.3oo. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * 48 * * | 0 2 0 2 | 1 3
xoo ... ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 0 1 0 1 2 0 | * * * 36 * | 0 0 4 0 | 0 4
... ... oxo ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 0 2 0 | * * * * 72 | 0 0 2 2 | 0 4
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ox. ... ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 0 | 2 3 0 0 0 | 24 * * * | 2 0
xo. ... ox.3oo. ...&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 1 | 0 3 2 0 0 | * 48 * * | 1 1
xoo ... oxo ... ...&#x & ♦ 3 2 | 1 6 2 1 | 0 2 3 1 4 0 | 0 1 0 2 2 | * * 72 * | 0 2
... ... oxo3ooo ...&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 1 | 0 0 2 0 3 | * * * 48 | 0 2
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ox.3oo. ...&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 1 | 3 9 3 0 0 | 3 3 0 0 | 16 *
xoo ... oxo3ooo ...&#x ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 1 | 0 3 3 3 6 | 0 1 3 2 | * 48
xoo3oox ooo3oxo3ooo&#xt → both heights = 1/sqrt(6) = 0.408248
({3} || pseudo perp oct || dual {3})
o..3o.. o..3o..3o.. & | 6 * ♦ 2 6 2 0 | 1 12 12 3 12 0 0 | 6 24 4 4 18 24 | 12 8 8 36 8 8 | 4 4 12 12
.o.3.o. .o.3.o.3.o. | * 6 ♦ 0 6 0 4 | 0 6 24 0 6 2 2 | 2 24 12 12 6 24 | 8 12 12 24 12 12 | 4 4 12 12
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
x.. ... ... ... ... & | 2 0 | 6 * * * ♦ 1 6 0 1 0 0 0 | 6 12 0 0 6 0 | 12 4 4 12 0 0 | 4 4 4 4
oo.3oo. oo.3oo.3oo.&#x & | 1 1 | * 36 * * ♦ 0 2 4 0 2 0 0 | 1 8 2 2 3 8 | 4 4 4 12 4 4 | 2 2 6 6
o.o3o.o o.o3o.o3o.o&#x | 2 0 | * * 6 * ♦ 0 0 0 2 6 0 0 | 0 0 0 0 12 12 | 0 0 0 24 4 4 | 0 0 8 8
... ... ... .x. ... | 0 2 | * * * 12 ♦ 0 0 6 0 0 1 1 | 0 6 6 6 0 6 | 2 6 6 6 6 6 | 2 2 6 6
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
x..3o.. ... ... ... & | 3 0 | 3 0 0 0 | 2 * * * * * * ♦ 6 0 0 0 0 0 | 12 0 0 0 0 0 | 4 4 0 0
xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | * 36 * * * * * ♦ 1 4 0 0 1 0 | 4 2 2 4 0 0 | 2 2 2 2
... ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | * * 72 * * * * ♦ 0 2 1 1 0 2 | 1 2 2 3 2 2 | 1 1 3 3
x.o ... ... ... ...&#x & | 3 0 | 1 0 2 0 | * * * 6 * * * ♦ 0 0 0 0 6 0 | 0 0 0 12 0 0 | 0 0 4 4
ooo3ooo ooo3ooo3ooo&#x | 2 1 | 0 2 1 0 | * * * * 36 * * ♦ 0 0 0 0 2 4 | 0 0 0 8 2 2 | 0 0 4 4
... ... .o.3.x. ... | 0 3 | 0 0 0 3 | * * * * * 4 * ♦ 0 0 6 0 0 0 | 0 6 0 0 6 0 | 2 0 6 0
... ... ... .x.3.o. | 0 3 | 0 0 0 3 | * * * * * * 4 ♦ 0 0 0 6 0 0 | 0 0 6 0 0 6 | 0 2 0 6
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 0 | 12 * * * * * | 4 0 0 0 0 0 | 2 2 0 0
xo. ... ... ox. ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 0 | * 72 * * * * | 1 1 1 1 0 0 | 1 1 1 1
... ... oo.3ox. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 0 | * * 24 * * * | 0 2 0 0 2 0 | 1 0 3 0
... ... ... ox.3oo.&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 0 1 | * * * 24 * * | 0 0 2 0 0 2 | 0 1 0 3
xoo ... ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 0 1 0 1 2 0 0 | * * * * 36 * | 0 0 0 4 0 0 | 0 0 2 2
... ... ... oxo ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 0 2 0 0 | * * * * * 72 | 0 0 0 2 1 1 | 0 0 2 2
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. ... ox. ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 0 0 | 2 3 0 0 0 0 | 24 * * * * * | 1 1 0 0
xo. ... oo.3ox. ...&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 1 0 | 0 3 2 0 0 0 | * 24 * * * * | 1 0 1 0
xo. ... ... ox.3oo.&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 0 1 | 0 3 0 2 0 0 | * * 24 * * * | 0 1 0 1
xoo ... ... oxo ...&#x & ♦ 3 2 | 1 6 2 1 | 0 2 3 1 4 0 0 | 0 1 0 0 2 2 | * * * 72 * * | 0 0 1 1
... ... ooo3oxo ...&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 1 0 | 0 0 2 0 0 3 | * * * * 24 * | 0 0 2 0
... ... ... oxo3ooo&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 0 1 | 0 0 0 2 0 3 | * * * * * 24 | 0 0 0 2
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. oo.3ox. ...&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 1 0 | 3 9 3 0 0 0 | 3 3 0 0 0 0 | 8 * * *
xo.3oo. ... ox.3oo.&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 0 1 | 3 9 0 3 0 0 | 3 0 3 0 0 0 | * 8 * *
xoo ... ooo3oxo ...&#x & ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 1 0 | 0 3 3 0 3 6 | 0 1 0 3 2 0 | * * 24 *
xoo ... ... oxo3ooo&#x & ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 0 1 | 0 3 0 3 3 6 | 0 0 1 3 0 2 | * * * 24
xo3oo4oo ox3oo4oo&#zx → height = 0
(tegum sum of 2 perp octs)
(tegum product of 2 octs)
o.3o.4o. o.3o.4o. | 6 * ♦ 4 6 0 | 4 24 12 0 | 24 48 8 | 48 32 | 32
.o3.o4.o .o3.o4.o | * 6 ♦ 0 6 4 | 0 12 24 4 | 8 48 24 | 32 48 | 32
---------------------+-----+----------+-----------+-----------+-------+---
x. .. .. .. .. .. | 2 0 | 12 * * ♦ 2 6 0 0 | 12 12 0 | 24 8 | 16
oo3oo4oo oo3oo4oo&#x | 1 1 | * 36 * ♦ 0 4 4 0 | 4 16 4 | 16 16 | 16
.. .. .. .x .. .. | 0 2 | * * 12 ♦ 0 0 6 2 | 0 12 12 | 8 24 | 16
---------------------+-----+----------+-----------+-----------+-------+---
x.3o. .. .. .. .. | 3 0 | 3 0 0 | 8 * * * ♦ 6 0 0 | 12 0 | 8
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 72 * * ♦ 2 4 0 | 8 4 | 8
.. .. .. ox .. ..&#x | 1 2 | 0 2 1 | * * 72 * ♦ 0 4 2 | 4 8 | 8
.. .. .. .x3.o .. | 0 3 | 0 0 3 | * * * 8 ♦ 0 0 6 | 0 12 | 8
---------------------+-----+----------+-----------+-----------+-------+---
xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | 48 * * | 4 0 | 4
xo .. .. ox .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * 144 * | 2 2 | 4
.. .. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * 48 | 0 4 | 4
---------------------+-----+----------+-----------+-----------+-------+---
xo3oo .. ox .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 2 3 0 | 96 * | 2
xo .. .. ox3oo ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 3 2 | * 96 | 2
---------------------+-----+----------+-----------+-----------+-------+---
xo3oo .. ox3oo ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 3 9 3 | 3 3 | 64
or
o.3o.4o. o.3o.4o. & | 12 ♦ 4 6 | 4 36 | 32 48 | 80 | 32
-----------------------+----+-------+--------+--------+-----+---
x. .. .. .. .. .. & | 2 | 24 * ♦ 2 6 | 12 12 | 32 | 16
oo3oo4oo oo3oo4oo&#x | 2 | * 36 ♦ 0 8 | 8 16 | 32 | 16
-----------------------+----+-------+--------+--------+-----+---
x.3o. .. .. .. .. & | 3 | 3 0 | 16 * ♦ 6 0 | 12 | 8
xo .. .. .. .. ..&#x & | 3 | 1 2 | * 144 ♦ 2 4 | 12 | 8
-----------------------+----+-------+--------+--------+-----+---
xo3oo .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | 96 * | 4 | 4
xo .. .. ox .. ..&#x ♦ 4 | 2 4 | 0 4 | * 144 | 4 | 4
-----------------------+----+-------+--------+--------+-----+---
xo3oo .. ox .. ..&#x & ♦ 5 | 4 6 | 1 9 | 2 3 | 192 | 2
-----------------------+----+-------+--------+--------+-----+---
xo3oo .. ox3oo ..&#x ♦ 6 | 6 9 | 2 18 | 6 9 | 6 | 64
oo3xo3oo oo3ox3oo&#zx → height = 0
(tegum sum of 2 perp octs)
(tegum product of 2 octs)
o.3o.3o. o.3o.3o. & | 12 ♦ 4 6 | 2 2 36 | 16 16 48 | 40 40 | 16 8 8
-----------------------+----+-------+---------+-----------+-------+---------
.. x.. .. .. .. .. & | 2 | 24 * ♦ 1 1 6 | 6 6 12 | 16 16 | 8 4 4
oo3oo3oo oo3oo3oo&#x | 2 | * 36 ♦ 0 0 8 | 4 4 16 | 16 16 | 8 4 4
-----------------------+----+-------+---------+-----------+-------+---------
o.3x. .. .. .. .. & | 3 | 3 0 | 8 * * ♦ 6 0 0 | 12 0 | 4 4 0
.. x.3o. .. .. .. & | 3 | 3 0 | * 8 * ♦ 0 6 0 | 0 12 | 4 0 4
.. xo .. .. .. ..&#x & | 3 | 1 2 | * * 144 ♦ 1 1 4 | 6 6 | 4 2 2
-----------------------+----+-------+---------+-----------+-------+---------
oo3xo .. .. .. ..&#x & ♦ 4 | 3 3 | 1 0 3 | 48 * * | 4 0 | 2 2 0
.. xo3oo .. .. ..&#x & ♦ 4 | 3 3 | 0 1 3 | * 48 * | 0 4 | 2 0 2
.. xo .. .. ox ..&#x ♦ 4 | 2 4 | 0 0 4 | * * 144 | 2 2 | 2 1 1
-----------------------+----+-------+---------+-----------+-------+---------
oo3xo .. .. ox ..&#x & ♦ 5 | 4 6 | 1 0 9 | 2 0 3 | 96 * | 1 1 0
.. xo3oo .. ox ..&#x & ♦ 5 | 4 6 | 0 1 9 | 0 2 3 | * 96 | 1 0 1
-----------------------+----+-------+---------+-----------+-------+---------
oo3xo .. oo3ox ..&#x & ♦ 6 | 6 9 | 1 1 18 | 3 3 9 | 3 3 | 32 * *
oo3xo .. .. ox3oo&#x ♦ 6 | 6 9 | 2 0 18 | 6 0 9 | 6 0 | * 16 *
.. xo3oo oo3ox ..&#x ♦ 6 | 6 9 | 0 2 18 | 0 6 9 | 0 6 | * * 16
xooo3oxoo ooxo3ooox&#x
(tegum product of 2 octs, where each (perp) factor in turn is represented as a lace prism)
o...3o... o...3o... | 12 ♦ 2 2 6 | 1 3 18 18 | 24 12 8 12 24 | 30 30 10 10 | 18 2 12
-------------------------+----+----------+------------+----------------+-------------+--------
x... .... .... .... & | 2 | 12 * * ♦ 1 1 0 6 | 6 0 6 6 6 | 12 6 8 6 | 6 2 8
oo..3oo.. oo..3oo..&#x & | 2 | * 12 * ♦ 0 2 6 0 | 12 6 0 0 6 | 12 18 0 2 | 12 0 4
o.o.3o.o. o.o.3o.o.&#x & | 2 | * * 36 ♦ 0 0 4 4 | 6 4 2 4 8 | 12 12 4 4 | 9 1 6
-------------------------+----+----------+------------+----------------+-------------+--------
x...3o... .... .... & | 3 | 3 0 0 | 4 * * * ♦ 0 0 6 0 0 | 0 0 6 6 | 0 2 6
xo.. .... .... ....&#x & | 3 | 1 2 0 | * 12 * * ♦ 6 0 0 0 0 | 6 6 0 0 | 6 0 2
ooo.3ooo. ooo.3ooo.&#x & | 3 | 0 1 2 | * * 72 * ♦ 2 2 0 0 2 | 4 7 0 1 | 6 0 2
x.o. .... .... ....&#x & | 3 | 1 0 2 | * * * 72 ♦ 1 0 1 2 2 | 5 2 3 2 | 3 1 4
-------------------------+----+----------+------------+----------------+-------------+--------
xoo. .... .... ....&#x & ♦ 4 | 1 2 3 | 0 1 2 1 | 72 * * * * | 2 2 0 0 | 3 0 1
oooo3oooo oooo3oooo&#x ♦ 4 | 0 2 4 | 0 0 4 0 | * 36 * * * | 0 4 0 0 | 4 0 0
x.o.3o.o. .... ....&#x & ♦ 4 | 3 0 3 | 1 0 0 3 | * * 24 * * | 0 0 2 2 | 0 1 3
x.o. .... o.x. ....&#x & ♦ 4 | 2 0 4 | 0 0 0 4 | * * * 36 * | 2 0 2 0 | 1 1 2
x.oo .... .... ....&#x & ♦ 4 | 1 1 4 | 0 0 2 2 | * * * * 72 | 2 1 0 1 | 2 0 2
-------------------------+----+----------+------------+----------------+-------------+--------
xoo. .... oox. ....&#x & ♦ 5 | 2 2 6 | 0 1 4 5 | 2 0 0 1 2 | 72 * * * | 1 0 1
xooo .... .... ....&#x & ♦ 5 | 1 3 6 | 0 1 7 2 | 2 2 0 0 1 | * 72 * * | 2 0 0
x.o.3o.o. o.x. ....&#x & ♦ 5 | 4 0 6 | 1 0 0 9 | 0 0 2 3 0 | * * 24 * | 0 1 1
x.oo3o.oo .... ....&#x & ♦ 5 | 3 1 6 | 1 0 3 6 | 0 0 2 0 3 | * * * 24 | 0 0 2
-------------------------+----+----------+------------+----------------+-------------+--------
xooo .... ooxo ....&#x & ♦ 6 | 2 4 9 | 0 2 12 6 | 6 4 0 1 4 | 2 4 0 0 | 36 * *
x.o.3o.o. o.x.3o.o.&#x & ♦ 6 | 6 0 9 | 2 0 0 18 | 0 0 6 9 0 | 0 0 6 0 | * 4 *
x.oo3o.oo o.xo ....&#x & ♦ 6 | 4 2 9 | 1 1 6 12 | 3 0 3 3 6 | 3 0 1 2 | * * 24
xooo3ooxo oxoo3ooox&#xr → all cyclical heights = 1/sqrt(3) = 0.577350
(in fact this lace simplex degenerates into a square)
o...3o... o...3o... | 12 ♦ 2 6 2 | 1 18 18 3 | 8 12 24 12 24 | 10 30 30 10 | 2 18 12
-------------------------+----+----------+------------+----------------+-------------+--------
x... .... .... .... & | 2 | 12 * * ♦ 1 6 0 1 | 6 6 6 0 6 | 8 12 6 6 | 2 6 8
oo..3oo.. oo..3oo..&#x & | 2 | * 36 * ♦ 0 4 4 0 | 2 4 6 4 8 | 4 12 12 4 | 1 9 6
o.o.3o.o. o.o.3o.o.&#x & | 2 | * * 12 ♦ 0 0 6 2 | 0 0 12 6 6 | 0 12 18 2 | 0 12 4
-------------------------+----+----------+------------+----------------+-------------+--------
x...3o... .... .... & | 3 | 3 0 0 | 4 * * * ♦ 6 0 0 0 0 | 6 0 0 6 | 2 0 6
xo.. .... .... ....&#x & | 3 | 1 2 0 | * 72 * * ♦ 1 2 1 0 2 | 3 5 2 2 | 1 3 4
ooo.3ooo. ooo.3ooo.&#x & | 3 | 0 2 1 | * * 72 * ♦ 0 0 2 2 2 | 0 4 7 1 | 0 6 2
x.o. .... .... ....&#x & | 3 | 1 0 2 | * * * 12 ♦ 0 0 6 0 0 | 0 6 6 0 | 0 6 2
-------------------------+----+----------+------------+----------------+-------------+--------
xo..3oo.. .... ....&#x & ♦ 4 | 3 3 0 | 1 3 0 0 | 24 * * * * | 2 0 0 2 | 1 0 3
xo.. .... ox.. ....&#x & ♦ 4 | 2 4 0 | 0 4 0 0 | * 36 * * * | 2 2 0 0 | 1 1 2
xoo. .... .... ....&#x & ♦ 4 | 1 3 2 | 0 1 2 1 | * * 72 * * | 0 2 2 0 | 0 3 1
oooo3oooo oooo3oooo&#x ♦ 4 | 0 4 2 | 0 0 4 0 | * * * 36 * | 0 0 4 0 | 0 4 0
xo.o .... .... ....&#x & ♦ 4 | 1 4 1 | 0 2 2 0 | * * * * 72 | 0 2 1 1 | 0 2 2
-------------------------+----+----------+------------+----------------+-------------+--------
xo..3oo.. ox.. ....&#x & ♦ 5 | 4 6 0 | 1 9 0 0 | 2 3 0 0 0 | 24 * * * | 1 0 1
xoo. .... oox. ....&#x & ♦ 5 | 2 6 2 | 0 5 4 1 | 0 1 2 0 2 | * 72 * * | 0 1 1
xooo .... .... ....&#x & ♦ 5 | 1 6 3 | 0 2 7 1 | 0 0 2 2 1 | * * 72 * | 0 2 0
xo.o3oo.o .... ....&#x & ♦ 5 | 3 6 1 | 1 6 3 0 | 2 0 0 0 3 | * * * 24 | 0 0 2
-------------------------+----+----------+------------+----------------+-------------+--------
xo..3oo.. ox..3oo..&#x & ♦ 6 | 6 9 0 | 2 18 0 0 | 6 9 0 0 0 | 6 0 0 0 | 4 * *
xooo .... ooxo ....&#x & ♦ 6 | 2 9 4 | 0 6 12 2 | 0 1 6 4 4 | 0 2 4 0 | * 36 *
xo.o3oo.o ox.o ....&#x & ♦ 6 | 4 9 2 | 1 12 6 1 | 3 3 3 0 6 | 1 3 0 2 | * * 24
xoo4ooo oxo4ooo oox4ooo&#zx → all heights = 0
(tegum sum of 3 pairwise orthogonal {4})
(tegum product of 3 {4})
o..4o.. o..4o.. o..4o.. & | 12 ♦ 2 8 | 24 16 | 16 64 | 80 | 32
------------------------------+----+-------+-------+--------+-----+---
x.. ... ... ... ... ... & | 2 | 12 * ♦ 8 0 | 8 16 | 32 | 16
oo.4oo. oo.4oo. oo.4oo.&#x & | 2 | * 48 ♦ 4 4 | 4 20 | 32 | 16
------------------------------+----+-------+-------+--------+-----+---
xo. ... ... ... ... ... & | 3 | 1 2 | 96 * ♦ 2 4 | 12 | 8
ooo4ooo ooo4ooo ooo4ooo&#x & | 3 | 0 3 | * 64 ♦ 0 6 | 12 | 8
------------------------------+----+-------+-------+--------+-----+---
xo. ... ox. ... ... ...&#x & ♦ 4 | 2 4 | 4 0 | 48 * | 4 | 4
xoo ... ... ... ... ...&#x & ♦ 4 | 1 5 | 2 2 | * 192 | 4 | 4
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... ... ...&#x & ♦ 5 | 2 8 | 6 4 | 1 4 | 192 | 2
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... oox ...&#x & ♦ 6 | 3 12 | 12 8 | 3 12 | 6 | 64
xoo xoo oxo oxo oox oox&#zx → all heights = 0
(tegum sum of 3 pairwise orthogonal {4})
(tegum product of 3 {4})
o.. o.. o.. o.. o.. o.. & | 12 ♦ 2 8 | 24 16 | 16 64 | 80 | 32
------------------------------+----+-------+-------+--------+-----+---
x.. ... ... ... ... ... & | 2 | 12 * ♦ 8 0 | 8 16 | 32 | 16
oo. oo. oo. oo. oo. oo.&#x & | 2 | * 48 ♦ 4 4 | 4 20 | 32 | 16
------------------------------+----+-------+-------+--------+-----+---
xo. ... ... ... ... ... & | 3 | 1 2 | 96 * ♦ 2 4 | 12 | 8
ooo ooo ooo ooo ooo ooo&#x & | 3 | 0 3 | * 64 ♦ 0 6 | 12 | 8
------------------------------+----+-------+-------+--------+-----+---
xo. ... ox. ... ... ...&#x & ♦ 4 | 2 4 | 4 0 | 48 * | 4 | 4
xoo ... ... ... ... ...&#x & ♦ 4 | 1 5 | 2 2 | * 192 | 4 | 4
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... ... ...&#x & ♦ 5 | 2 8 | 6 4 | 1 4 | 192 | 2
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... oox ...&#x & ♦ 6 | 3 12 | 12 8 | 3 12 | 6 | 64
