|
Acronym
|
hesa (old: hiss)
|
|
Name
|
hemihepteract,
vertex figure of bay,
Gosset polytope 14,1
|
|
Circumradius
|
sqrt(7/8) = 0.935414
|
Inradius
wrt. hop
|
5/sqrt(56) = 0.668153
|
Inradius
wrt. hax
|
1/sqrt(8) = 0.353553
|
Lace city
in approx. ASCII-art
|
 ©
|
H h where:
H = x3o3o *b3o3o (hin)
h H h = o3o3x *b3o3o (alt. hin)
| |
| +- o3o3x *b3o3o3o (hax)
+----- x3o3o *b3o3o3o (alt. hax)
|
|
o R r o -- o3o3x *b3o3o3o (hax)
H D h -- x3o3o *b3o3o3o (alt. hax)
\ \ \ \
\ \ \ +- o3o3o3o3o3o (point)
\ \ +---- o3x3o3o3o3o (ril)
\ +------- o3o3o3x3o3o (inv. bril)
+---------- o3o3o3o3o3x (dual hop)
where:
o = o3o3o3o3o (point)
H = x3o3o3o3o (hix)
R = o3x3o3o3o (rix)
D = o3o3x3o3o (dot)
r = o3o3o3x3o (inv. rix)
h = o3o3o3o3x (dual hix)
|
Lace hyper city
in approx. ASCII-art
|
_E---------_O
O----------E |
| | | |
| | | |
| | | |
| _O-------|-_E
E----------O
where:
E = x3o3o *b3o (hex)
O = o3o3x *b3o (gyro hex)
|
|
Coordinates
|
(1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all permutations, all even changes of sign
|
|
Volume
|
311 sqrt(2)/5040 = 0.087266
|
|
Surface
|
[301+2 sqrt(7)]/180 = 1.701619
|
Dihedral angles
(at margins)
|
- at hix between hax and hop: arccos[-1/sqrt(7)] = 112.207654°
- at hin between hax and hax: 90°
|
|
Face vector
|
64, 672, 2240, 2800, 1624, 532, 78
|
|
Confer
|
- uniform relative:
-
tethex
- related segmentoexa:
-
rilpy
rilalbril
hopabril
hexal trahex
hinaf
- general polytopal classes:
-
Wythoffian polyexa
segmentoexa
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
-
demihypercube Dn
|
External
links
|
|
Incidence matrix according to Dynkin symbol
x3o3o *b3o3o3o3o
. . . . . . . | 64 ♦ 21 | 105 | 35 140 | 35 105 | 21 42 | 7 7
-----------------+----+-----+------+----------+----------+--------+------
x . . . . . . | 2 | 672 ♦ 10 | 5 20 | 10 20 | 10 10 | 5 2
-----------------+----+-----+------+----------+----------+--------+------
x3o . . . . . | 3 | 3 | 2240 | 1 4 | 4 6 | 6 4 | 4 1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o . . . . ♦ 4 | 6 | 4 | 560 * ♦ 4 0 | 6 0 | 4 0
x3o . *b3o . . . ♦ 4 | 6 | 4 | * 2240 | 1 3 | 3 3 | 3 1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o . . . ♦ 8 | 24 | 32 | 8 8 | 280 * | 3 0 | 3 0
x3o . *b3o3o . . ♦ 5 | 10 | 10 | 0 5 | * 1344 | 1 2 | 2 1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o3o . . ♦ 16 | 80 | 160 | 40 80 | 10 16 | 84 * | 2 0
x3o . *b3o3o3o . ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 448 | 1 1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o3o3o . ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 | 14 *
x3o . *b3o3o3o3o ♦ 7 | 21 | 35 | 0 35 | 0 21 | 0 7 | * 64
o3o3o3o3o3o4s
demi( . . . . . . . ) | 64 ♦ 21 | 105 | 35 140 | 35 105 | 21 42 | 7 7
----------------------+----+-----+------+----------+----------+--------+------
. . . . . o4s | 2 | 672 ♦ 10 | 5 20 | 10 20 | 10 10 | 5 2
----------------------+----+-----+------+----------+----------+--------+------
sefa( . . . . o3o4s ) | 3 | 3 | 2240 | 1 4 | 4 6 | 6 4 | 4 1
----------------------+----+-----+------+----------+----------+--------+------
. . . . o3o4s ♦ 4 | 6 | 4 | 560 * ♦ 4 0 | 6 0 | 4 0
sefa( . . . o3o3o4s ) ♦ 4 | 6 | 4 | * 2240 | 1 3 | 3 3 | 3 1
----------------------+----+-----+------+----------+----------+--------+------
. . . o3o3o4s ♦ 8 | 24 | 32 | 8 8 | 280 * | 3 0 | 3 0
sefa( . . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 1344 | 1 2 | 2 1
----------------------+----+-----+------+----------+----------+--------+------
. . o3o3o3o4s ♦ 16 | 80 | 160 | 40 80 | 10 16 | 84 * | 2 0
sefa( . o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 448 | 1 1
----------------------+----+-----+------+----------+----------+--------+------
. o3o3o3o3o4s ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 | 14 *
sefa( o3o3o3o3o3o4s ) ♦ 7 | 21 | 35 | 0 35 | 0 21 | 0 7 | * 64
starting figure: o3o3o3o3o3o4x
xo3oo3ox *b3oo3oo3oo&#x → height = 1/sqrt(2) = 0.707107
(hax || alt hax)
o.3o.3o. *b3o.3o.3o. | 32 * ♦ 15 6 0 | 60 30 15 0 | 20 60 60 15 20 0 0 | 15 30 20 60 15 0 0 | 6 6 15 30 6 0 0 | 1 6 6 1 0
.o3.o3.o *b3.o3.o3.o | * 32 ♦ 0 6 15 | 0 15 30 60 | 0 0 20 15 60 20 60 | 0 0 20 15 60 15 30 | 0 0 15 6 30 6 6 | 0 6 1 6 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x. .. .. .. .. .. | 2 0 | 240 * * ♦ 8 2 0 0 | 4 12 8 1 0 0 0 | 6 8 4 12 0 0 0 | 4 2 6 8 0 0 0 | 1 4 2 0 0
oo3oo3oo *b3oo3oo3oo&#x | 1 1 | * 192 * ♦ 0 5 5 0 | 0 0 10 5 10 0 0 | 0 0 10 10 10 0 0 | 0 0 10 5 5 0 0 | 0 5 1 1 0
.. .. .x .. .. .. | 0 2 | * * 240 ♦ 0 0 2 8 | 0 0 0 1 8 4 12 | 0 0 4 0 12 6 8 | 0 0 6 0 8 4 2 | 0 4 0 2 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o. .. .. .. .. | 3 0 | 3 0 0 | 640 * * * | 1 3 1 0 0 0 0 | 3 3 1 3 0 0 0 | 3 1 3 3 0 0 0 | 1 3 1 0 0
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 480 * * | 0 0 4 1 0 0 0 | 0 0 4 6 0 0 0 | 0 0 6 4 0 0 0 | 0 4 1 0 0
.. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * * 480 * | 0 0 0 1 4 0 0 | 0 0 4 0 6 0 0 | 0 0 6 0 4 0 0 | 0 4 0 1 0
.. .o3.x .. .. .. | 0 3 | 0 0 3 | * * * 640 | 0 0 0 0 1 1 3 | 0 0 1 0 3 3 3 | 0 0 3 0 3 3 1 | 0 3 0 1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 160 * * * * * * ♦ 3 0 1 0 0 0 0 | 3 0 3 0 0 0 0 | 1 3 0 0 0
x.3o. .. *b3o. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | * 480 * * * * * | 1 2 0 1 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0 0
xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * * 640 * * * * | 0 0 1 3 0 0 0 | 0 0 3 3 0 0 0 | 0 3 1 0 0
xo .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * * 240 * * * ♦ 0 0 4 0 0 0 0 | 0 0 6 0 0 0 0 | 0 4 0 0 0
.. oo3ox .. .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * * 640 * * | 0 0 1 0 3 0 0 | 0 0 3 0 3 0 0 | 0 3 0 1 0
.o3.o3.x .. .. .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * * 160 * ♦ 0 0 1 0 0 3 0 | 0 0 3 0 0 3 0 | 0 3 0 0 1
.. .o3.x *b3.o .. .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * * * 480 | 0 0 0 0 1 1 2 | 0 0 1 0 2 2 1 | 0 2 0 1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. *b3o. .. .. ♦ 8 0 | 24 0 0 | 32 0 0 0 | 8 8 0 0 0 0 0 | 60 * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0 0
x.3o. .. *b3o.3o. .. ♦ 5 0 | 10 0 0 | 10 0 0 0 | 0 5 0 0 0 0 0 | * 192 * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 0
xo3oo3ox .. .. ..&#x ♦ 4 4 | 6 12 6 | 4 12 12 4 | 1 0 4 6 4 1 0 | * * 160 * * * * | 0 0 3 0 0 0 0 | 0 3 0 0 0
xo3oo .. *b3oo .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 0 1 4 0 0 0 0 | * * * 480 * * * | 0 0 1 2 0 0 0 | 0 2 1 0 0
.. oo3ox *b3oo .. ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 0 4 0 1 | * * * * 480 * * | 0 0 1 0 2 0 0 | 0 2 0 1 0
.o3.o3.x *b3.o .. .. ♦ 0 8 | 0 0 24 | 0 0 0 32 | 0 0 0 0 0 8 8 | * * * * * 60 * | 0 0 1 0 0 2 0 | 0 2 0 0 1
.. .o3.x *b3.o3.o .. ♦ 0 5 | 0 0 10 | 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * 192 | 0 0 0 0 1 1 1 | 0 1 0 1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. *b3o.3o. .. ♦ 16 0 | 80 0 0 | 160 0 0 0 | 40 80 0 0 0 0 0 | 10 16 0 0 0 0 0 | 12 * * * * * * | 1 1 0 0 0
x.3o. .. *b3o.3o.3o. ♦ 6 0 | 15 0 0 | 20 0 0 0 | 0 15 0 0 0 0 0 | 0 6 0 0 0 0 0 | * 32 * * * * * | 1 0 1 0 0
xo3oo3ox *b3oo .. ..&#x ♦ 8 8 | 24 32 24 | 32 48 48 32 | 8 8 32 24 32 8 8 | 1 0 8 8 8 1 0 | * * 60 * * * * | 0 2 0 0 0
xo3oo .. *b3oo3oo ..&#x ♦ 5 1 | 10 5 0 | 10 10 0 0 | 0 5 10 0 0 0 0 | 0 1 0 5 0 0 0 | * * * 192 * * * | 0 1 1 0 0
.. oo3ox *b3oo3oo ..&#x ♦ 1 5 | 0 5 10 | 0 0 10 10 | 0 0 0 0 10 0 5 | 0 0 0 0 5 0 1 | * * * * 192 * * | 0 1 0 1 0
.o3.o3.x *b3.o3.o .. ♦ 0 16 | 0 0 80 | 0 0 0 160 | 0 0 0 0 0 40 80 | 0 0 0 0 0 10 16 | * * * * * 12 * | 0 1 0 0 1
.. .o3.x *b3.o3.o3.o ♦ 0 6 | 0 0 15 | 0 0 0 20 | 0 0 0 0 0 0 15 | 0 0 0 0 0 0 6 | * * * * * * 32 | 0 0 0 1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. *b3o.3o.3o. ♦ 32 0 | 240 0 0 | 640 0 0 0 | 160 480 0 0 0 0 0 | 60 192 0 0 0 0 0 | 12 32 0 0 0 0 0 | 1 * * * *
xo3oo3ox *b3oo3oo ..&#x ♦ 16 16 | 80 80 80 | 160 160 160 160 | 40 80 160 80 160 40 80 | 10 16 40 80 80 10 16 | 1 0 10 16 16 1 0 | * 12 * * *
xo3oo .. *b3oo3oo3oo&#x ♦ 6 1 | 15 6 0 | 20 15 0 0 | 0 15 20 0 0 0 0 | 0 6 0 15 0 0 0 | 0 1 0 6 0 0 0 | * * 32 * *
.. oo3ox *b3oo3oo3oo&#x ♦ 1 6 | 0 6 15 | 0 0 15 20 | 0 0 0 0 20 0 15 | 0 0 0 0 15 0 6 | 0 0 0 0 6 0 1 | * * * 32 *
.o3.o3.x *b3.o3.o3.o ♦ 0 32 | 0 0 240 | 0 0 0 640 | 0 0 0 0 0 160 480 | 0 0 0 0 0 60 192 | 0 0 0 0 0 12 32 | * * * * 1
oooo3oxoo3oooo3ooxo3oooo3ooox&#xt → all heights = sqrt(2/7) = 0.534522
(pt || (pseudo) ril || (pseudo) inv bril || dual hop)
o...3o...3o...3o...3o...3o... | 1 * * * ♦ 21 0 0 0 0 0 | 105 0 0 0 0 0 0 0 0 0 | 35 140 0 0 0 0 0 0 0 0 0 0 0 0 0 | 35 105 0 0 0 0 0 0 0 0 0 0 0 | 21 42 0 0 0 0 0 0 0 0 | 7 7 0 0 0 0
.o..3.o..3.o..3.o..3.o..3.o.. | * 21 * * ♦ 1 10 10 0 0 0 | 10 5 20 40 30 0 0 0 0 0 | 5 20 20 20 20 60 10 20 0 0 0 0 0 0 0 | 10 20 10 30 20 40 5 5 0 0 0 0 0 | 10 10 2 20 10 10 1 0 0 0 | 5 2 5 2 0 0
..o.3..o.3..o.3..o.3..o.3..o. | * * 35 * ♦ 0 0 6 12 3 0 | 0 0 0 12 36 18 12 24 3 0 | 0 0 0 4 4 36 18 36 12 4 36 12 12 1 0 | 1 0 0 12 12 36 18 12 3 24 18 4 0 | 3 0 0 12 12 12 6 6 12 0 | 3 0 4 4 3 0
...o3...o3...o3...o3...o3...o | * * * 7 ♦ 0 0 0 0 15 6 | 0 0 0 0 0 0 0 60 30 15 | 0 0 0 0 0 0 0 0 0 0 60 20 60 15 20 | 0 0 0 0 0 0 15 0 0 30 60 20 25 | 0 0 0 0 6 0 15 6 30 6 | 1 0 0 6 6 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
oo..3oo..3oo..3oo..3oo..3oo..&#x | 1 1 0 0 | 21 * * * * * ♦ 10 0 0 0 0 0 0 0 0 0 | 5 20 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10 20 0 0 0 0 0 0 0 0 0 0 0 | 10 10 0 0 0 0 0 0 0 0 | 5 2 0 0 0 0
.... .x.. .... .... .... .... | 0 2 0 0 | * 105 * * * * ♦ 1 1 4 4 0 0 0 0 0 0 | 1 4 6 4 4 6 0 0 0 0 0 0 0 0 0 | 4 6 4 6 6 4 0 0 0 0 0 0 0 | 6 4 1 4 4 1 0 0 0 0 | 4 1 1 1 0 0
.oo.3.oo.3.oo.3.oo.3.oo.3.oo.&#x | 0 1 1 0 | * * 210 * * * ♦ 0 0 0 4 6 0 0 0 0 0 | 0 0 0 2 2 12 3 6 0 0 0 0 0 0 0 | 1 0 0 6 6 12 3 2 0 0 0 0 0 | 3 0 0 6 6 4 1 0 0 0 | 3 0 2 2 0 0
.... .... .... ..x. .... .... | 0 0 2 0 | * * * 210 * * ♦ 0 0 0 0 3 3 2 2 0 0 | 0 0 0 0 0 3 3 6 3 1 6 2 1 0 0 | 0 0 0 1 3 6 6 3 1 6 3 1 0 | 1 0 0 2 6 3 3 2 3 0 | 2 0 1 3 1 0
..oo3..oo3..oo3..oo3..oo3..oo&#x | 0 0 1 1 | * * * * 105 * ♦ 0 0 0 0 0 0 0 8 2 0 | 0 0 0 0 0 0 0 0 0 0 12 4 8 1 0 | 0 0 0 0 0 0 6 0 0 8 12 4 0 | 0 0 0 0 4 0 6 2 8 0 | 1 0 0 4 2 0
.... .... .... .... .... ...x | 0 0 0 2 | * * * * * 21 ♦ 0 0 0 0 0 0 0 0 5 5 | 0 0 0 0 0 0 0 0 0 0 0 0 10 5 10 | 0 0 0 0 0 0 0 0 0 0 10 10 10 | 0 0 0 0 0 0 10 0 5 5 | 0 0 0 5 1 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
.... ox.. .... .... .... ....&#x | 1 2 0 0 | 2 1 0 0 0 0 | 105 * * * * * * * * * | 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 6 0 0 0 0 0 0 0 0 0 0 0 | 6 4 0 0 0 0 0 0 0 0 | 4 1 0 0 0 0
.o..3.x.. .... .... .... .... | 0 3 0 0 | 0 3 0 0 0 0 | * 35 * * * * * * * * | 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 | 4 0 0 6 0 0 0 0 0 0 0 0 0 | 6 0 0 4 0 0 0 0 0 0 | 4 0 1 0 0 0
.... .x..3.o.. .... .... .... | 0 3 0 0 | 0 3 0 0 0 0 | * * 140 * * * * * * * | 0 1 3 0 1 0 0 0 0 0 0 0 0 0 0 | 1 3 3 0 3 0 0 0 0 0 0 0 0 | 3 3 1 0 3 0 0 0 0 0 | 3 1 0 1 0 0
.... .xo. .... .... .... ....&#x | 0 2 1 0 | 0 1 2 0 0 0 | * * * 420 * * * * * * | 0 0 0 1 1 3 0 0 0 0 0 0 0 0 0 | 1 0 0 3 3 3 0 0 0 0 0 0 0 | 3 0 0 3 3 1 0 0 0 0 | 3 0 1 1 0 0
.... .... .... .ox. .... ....&#x | 0 1 2 0 | 0 0 2 1 0 0 | * * * * 630 * * * * * | 0 0 0 0 0 2 1 2 0 0 0 0 0 0 0 | 0 0 0 1 2 1 2 1 0 0 0 0 0 | 1 0 0 2 4 2 1 0 0 0 | 2 0 1 2 0 0
.... .... ..o.3..x. .... .... | 0 0 3 0 | 0 0 0 3 0 0 | * * * * * 210 * * * * | 0 0 0 0 0 0 1 0 2 0 2 0 0 0 0 | 0 0 0 0 2 0 2 0 1 4 1 0 0 | 1 0 0 0 4 0 1 2 2 0 | 2 0 0 2 1 0
.... .... .... ..x.3..o. .... | 0 0 3 0 | 0 0 0 3 0 0 | * * * * * * 140 * * * | 0 0 0 0 0 0 0 3 0 1 0 1 0 0 0 | 0 0 0 0 0 3 3 3 0 0 0 1 0 | 0 0 0 1 3 3 3 0 0 0 | 1 0 1 3 0 0
.... .... .... ..xo .... ....&#x | 0 0 2 1 | 0 0 0 1 2 0 | * * * * * * * 420 * * | 0 0 0 0 0 0 0 0 0 0 3 1 1 0 0 | 0 0 0 0 0 0 3 0 0 3 3 1 0 | 0 0 0 0 3 0 3 1 3 0 | 1 0 0 3 1 0
.... .... .... .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 2 1 | * * * * * * * * 105 * | 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 | 0 0 0 0 0 0 0 0 0 0 6 4 0 | 0 0 0 0 0 0 6 0 4 0 | 0 0 0 4 1 0
.... .... .... .... ...o3...x | 0 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 35 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 | 0 0 0 0 0 0 0 0 0 0 0 4 6 | 0 0 0 0 0 0 6 0 0 4 | 0 0 0 4 0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
oo..3ox.. .... .... .... ....&#x ♦ 1 3 0 0 | 3 3 0 0 0 0 | 3 1 0 0 0 0 0 0 0 0 | 35 * * * * * * * * * * * * * * ♦ 4 0 0 0 0 0 0 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 0 0 | 4 0 0 0 0 0
.... ox..3oo.. .... .... ....&#x ♦ 1 3 0 0 | 3 3 0 0 0 0 | 3 0 1 0 0 0 0 0 0 0 | * 140 * * * * * * * * * * * * * | 1 3 0 0 0 0 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 | 3 1 0 0 0 0
.... .x..3.o..3.o.. .... .... ♦ 0 4 0 0 | 0 6 0 0 0 0 | 0 0 4 0 0 0 0 0 0 0 | * * 105 * * * * * * * * * * * * | 0 1 2 0 1 0 0 0 0 0 0 0 0 | 1 2 1 0 2 0 0 0 0 0 | 2 1 0 1 0 0
.oo.3.xo. .... .... .... ....&#x ♦ 0 3 1 0 | 0 3 3 0 0 0 | 0 1 0 3 0 0 0 0 0 0 | * * * 140 * * * * * * * * * * * | 1 0 0 3 0 0 0 0 0 0 0 0 0 | 3 0 0 3 0 0 0 0 0 0 | 3 0 1 0 0 0
.... .xo.3.oo. .... .... ....&#x ♦ 0 3 1 0 | 0 3 3 0 0 0 | 0 0 1 3 0 0 0 0 0 0 | * * * * 140 * * * * * * * * * * ♦ 1 0 0 0 3 0 0 0 0 0 0 0 0 | 3 0 0 0 3 0 0 0 0 0 | 3 0 0 1 0 0
.... .xo. .... .ox. .... ....&#x ♦ 0 2 2 0 | 0 1 4 1 0 0 | 0 0 0 2 2 0 0 0 0 0 | * * * * * 630 * * * * * * * * * | 0 0 0 1 1 2 0 0 0 0 0 0 0 | 1 0 0 2 2 1 0 0 0 0 | 2 0 1 1 0 0
.... .... .oo.3.ox. .... ....&#x ♦ 0 1 3 0 | 0 0 3 3 0 0 | 0 0 0 0 3 1 0 0 0 0 | * * * * * * 210 * * * * * * * * ♦ 0 0 0 0 2 0 2 0 0 0 0 0 0 | 1 0 0 0 4 0 1 0 0 0 | 2 0 0 2 0 0
.... .... .... .ox.3.oo. ....&#x ♦ 0 1 3 0 | 0 0 3 3 0 0 | 0 0 0 0 3 0 1 0 0 0 | * * * * * * * 420 * * * * * * * | 0 0 0 0 0 2 1 1 0 0 0 0 0 | 0 0 0 1 2 2 1 0 0 0 | 1 0 1 2 0 0
.... ..o.3..o.3..x. .... .... ♦ 0 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 0 0 | * * * * * * * * 105 * * * * * * | 0 0 0 0 1 0 0 0 1 2 0 0 0 | 1 0 0 0 2 0 0 2 1 0 | 2 0 0 1 1 0
.... .... .... ..x.3..o.3..o. ♦ 0 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 0 4 0 0 0 | * * * * * * * * * 35 * * * * * | 0 0 0 0 0 0 0 3 0 0 0 1 0 | 0 0 0 0 0 3 3 0 0 0 | 0 0 1 3 0 0
.... .... ..oo3..xo .... ....&#x ♦ 0 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 0 1 0 3 0 0 | * * * * * * * * * * 420 * * * * | 0 0 0 0 0 0 1 0 0 2 1 0 0 | 0 0 0 0 2 0 1 1 2 0 | 1 0 0 2 1 0
.... .... .... ..xo3..oo ....&#x ♦ 0 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 0 0 1 3 0 0 | * * * * * * * * * * * 140 * * * ♦ 0 0 0 0 0 0 3 0 0 0 0 1 0 | 0 0 0 0 3 0 3 0 0 0 | 1 0 0 3 0 0
.... .... .... ..xo .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * 210 * * | 0 0 0 0 0 0 0 0 0 0 3 1 0 | 0 0 0 0 0 0 3 0 3 0 | 0 0 0 3 1 0
.... .... .... .... ..oo3..ox&#x ♦ 0 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * * * 35 * ♦ 0 0 0 0 0 0 0 0 0 0 0 4 0 | 0 0 0 0 0 0 6 0 0 0 | 0 0 0 4 0 0
.... .... .... ...o3...o3...x ♦ 0 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * 35 | 0 0 0 0 0 0 0 0 0 0 0 1 3 | 0 0 0 0 0 0 3 0 0 3 | 0 0 0 3 0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
ooo.3oxo.3ooo. .... .... ....&#xt ♦ 1 6 1 0 | 6 12 6 0 0 0 | 12 4 4 12 0 0 0 0 0 0 | 4 4 0 4 4 0 0 0 0 0 0 0 0 0 0 | 35 * * * * * * * * * * * * | 3 0 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0
.... ox..3oo..3oo.. .... ....&#x ♦ 1 4 0 0 | 4 6 0 0 0 0 | 6 0 4 0 0 0 0 0 0 0 | 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 | * 105 * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 | 2 1 0 0 0 0
.... .x..3.o..3.o..3.o.. .... ♦ 0 5 0 0 | 0 10 0 0 0 0 | 0 0 10 0 0 0 0 0 0 0 | 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 | * * 42 * * * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 | 1 1 0 1 0 0
.oo.3.xo. .... .ox. .... ....&#x ♦ 0 3 2 0 | 0 3 6 1 0 0 | 0 1 0 6 3 0 0 0 0 0 | 0 0 0 2 0 3 0 0 0 0 0 0 0 0 0 | * * * 210 * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 2 0 1 0 0 0
.... .xo.3.oo.3.ox. .... ....&#x ♦ 0 4 4 0 | 0 6 12 6 0 0 | 0 0 4 12 12 4 0 0 0 0 | 0 0 1 0 4 6 4 0 1 0 0 0 0 0 0 | * * * * 105 * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 | 2 0 0 1 0 0
.... .xo. .... .ox.3.oo. ....&#x ♦ 0 2 3 0 | 0 1 6 3 0 0 | 0 0 0 3 6 0 1 0 0 0 | 0 0 0 0 0 3 0 2 0 0 0 0 0 0 0 | * * * * * 420 * * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 1 0 1 1 0 0
.... .... .ooo3.oxo3.ooo ....&#xt ♦ 0 1 6 1 | 0 0 6 12 6 0 | 0 0 0 0 12 4 4 12 0 0 | 0 0 0 0 0 0 4 4 0 0 4 4 0 0 0 | * * * * * * 105 * * * * * * | 0 0 0 0 2 0 1 0 0 0 | 1 0 0 2 0 0
.... .... .... .ox.3.oo.3.oo.&#x ♦ 0 1 4 0 | 0 0 4 6 0 0 | 0 0 0 0 6 0 4 0 0 0 | 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 | * * * * * * * 105 * * * * * | 0 0 0 0 0 2 1 0 0 0 | 0 0 1 2 0 0
..o.3..o.3..o.3..x. .... .... ♦ 0 0 5 0 | 0 0 0 10 0 0 | 0 0 0 0 0 10 0 0 0 0 | 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 | * * * * * * * * 21 * * * * | 1 0 0 0 0 0 0 2 0 0 | 2 0 0 0 1 0
.... ..oo3..oo3..xo .... ....&#x ♦ 0 0 4 1 | 0 0 0 6 4 0 | 0 0 0 0 0 4 0 6 0 0 | 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 | * * * * * * * * * 210 * * * | 0 0 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0
.... .... ..oo3..xo .... ..ox&#x ♦ 0 0 3 2 | 0 0 0 3 6 1 | 0 0 0 0 0 1 0 6 3 0 | 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0 | * * * * * * * * * * 210 * * | 0 0 0 0 0 0 1 0 2 0 | 0 0 0 2 1 0
.... .... .... ..xo3..oo3..ox&#x ♦ 0 0 4 4 | 0 0 0 6 12 6 | 0 0 0 0 0 0 4 12 12 4 | 0 0 0 0 0 0 0 0 0 1 0 4 6 4 1 | * * * * * * * * * * * 35 * | 0 0 0 0 0 0 3 0 0 0 | 0 0 0 3 0 0
.... .... ...o3...o3...o3...x ♦ 0 0 0 5 | 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 | * * * * * * * * * * * * 21 | 0 0 0 0 0 0 1 0 0 2 | 0 0 0 2 0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
ooo.3oxo.3ooo.3oox. .... ....&#xt ♦ 1 10 5 0 | 10 30 30 10 0 0 | 30 10 20 60 30 10 0 0 0 0 | 10 20 5 20 20 30 10 0 5 0 0 0 0 0 0 | 5 5 0 10 5 0 0 0 1 0 0 0 0 | 21 * * * * * * * * * | 2 0 0 0 0 0
.... ox..3oo..3oo..3oo.. ....&#x ♦ 1 5 0 0 | 5 10 0 0 0 0 | 10 0 10 0 0 0 0 0 0 0 | 0 10 5 0 0 0 0 0 0 0 0 0 0 0 0 | 0 5 1 0 0 0 0 0 0 0 0 0 0 | * 42 * * * * * * * * | 1 1 0 0 0 0
.... .x..3.o..3.o..3.o..3.o.. ♦ 0 6 0 0 | 0 15 0 0 0 0 | 0 0 20 0 0 0 0 0 0 0 | 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 6 0 0 0 0 0 0 0 0 0 0 | * * 7 * * * * * * * | 0 1 0 1 0 0
.oo.3.xo. .... .ox.3.oo. ....&#x ♦ 0 3 3 0 | 0 3 9 3 0 0 | 0 1 0 9 9 0 1 0 0 0 | 0 0 0 3 0 9 0 3 0 0 0 0 0 0 0 | 0 0 0 3 0 3 0 0 0 0 0 0 0 | * * * 140 * * * * * * | 1 0 1 0 0 0
.... .xoo3.ooo3.oxo3.ooo ....&#xt ♦ 0 5 10 1 | 0 10 30 30 10 0 | 0 0 10 30 60 20 10 30 0 0 | 0 0 5 0 10 30 20 20 5 0 20 10 0 0 0 | 0 0 1 0 5 10 5 0 0 5 0 0 0 | * * * * 42 * * * * * | 1 0 0 1 0 0
.... .xo. .... .ox.3.oo.3.oo.&#x ♦ 0 2 4 0 | 0 1 8 6 0 0 | 0 0 0 4 12 0 4 0 0 0 | 0 0 0 0 0 6 0 8 0 1 0 0 0 0 0 | 0 0 0 0 0 4 0 2 0 0 0 0 0 | * * * * * 105 * * * * | 0 0 1 1 0 0
.... .... .ooo3.oxo3.ooo3.oox&#xt ♦ 0 1 10 5 | 0 0 10 30 30 10 | 0 0 0 0 30 10 20 60 30 10 | 0 0 0 0 0 0 10 20 0 5 20 20 30 10 5 | 0 0 0 0 0 0 5 5 0 0 10 5 1 | * * * * * * 21 * * * | 0 0 0 2 0 0
..oo3..oo3..oo3..xo .... ....&#x ♦ 0 0 5 1 | 0 0 0 10 5 0 | 0 0 0 0 0 10 0 10 0 0 | 0 0 0 0 0 0 0 0 5 0 10 0 0 0 0 | 0 0 0 0 0 0 0 0 1 5 0 0 0 | * * * * * * * 42 * * | 1 0 0 0 1 0
.... ..oo3..oo3..xo .... ..ox&#x ♦ 0 0 4 2 | 0 0 0 6 8 1 | 0 0 0 0 0 4 0 12 4 0 | 0 0 0 0 0 0 0 0 1 0 8 0 6 0 0 | 0 0 0 0 0 0 0 0 0 2 4 0 0 | * * * * * * * * 105 * | 0 0 0 1 1 0
.... ...o3...o3...o3...o3...x ♦ 0 0 0 6 | 0 0 0 0 0 15 | 0 0 0 0 0 0 0 0 0 20 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 | 0 0 0 0 0 0 0 0 0 0 0 0 6 | * * * * * * * * * 7 | 0 0 0 1 0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
oooo3oxoo3oooo3ooxo3oooo ....&#xt ♦ 1 15 15 1 | 15 60 90 60 15 0 | 60 20 60 180 180 60 20 60 0 0 | 20 60 30 60 60 180 60 60 30 0 60 20 0 0 0 | 15 30 6 60 30 60 15 0 6 30 0 0 0 | 6 6 0 20 6 0 0 6 0 0 | 7 * * * * *
.... ox..3oo..3oo..3oo..3oo..&#x ♦ 1 6 0 0 | 6 15 0 0 0 0 | 15 0 20 0 0 0 0 0 0 0 | 0 20 15 0 0 0 0 0 0 0 0 0 0 0 0 | 0 15 6 0 0 0 0 0 0 0 0 0 0 | 0 6 1 0 0 0 0 0 0 0 | * 7 * * * *
.oo.3.xo. .... .ox.3.oo.3.oo.&#x ♦ 0 3 4 0 | 0 3 12 6 0 0 | 0 1 0 12 18 0 4 0 0 0 | 0 0 0 4 0 18 0 12 0 1 0 0 0 0 0 | 0 0 0 6 0 12 0 3 0 0 0 0 0 | 0 0 0 4 0 3 0 0 0 0 | * * 35 * * *
.... .xoo3.ooo3.oxo3.ooo3.oox&#xt ♦ 0 6 20 6 | 0 15 60 90 60 15 | 0 0 20 60 180 60 60 180 60 20 | 0 0 15 0 20 90 60 120 15 15 120 60 90 20 15 | 0 0 6 0 15 60 30 30 0 30 60 15 6 | 0 0 1 0 6 15 6 0 15 1 | * * * 7 * *
..oo3..oo3..oo3..xo .... ..ox&#x ♦ 0 0 5 2 | 0 0 0 10 10 1 | 0 0 0 0 0 10 0 20 5 0 | 0 0 0 0 0 0 0 0 5 0 20 0 10 0 0 | 0 0 0 0 0 0 0 0 1 10 10 0 0 | 0 0 0 0 0 0 0 2 5 0 | * * * * 21 *
...o3...o3...o3...o3...o3...x ♦ 0 0 0 7 | 0 0 0 0 0 21 | 0 0 0 0 0 0 0 0 0 35 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 | 0 0 0 0 0 0 0 0 0 0 0 0 21 | 0 0 0 0 0 0 0 0 0 7 | * * * * * 1
oxoo3ooxo xoxo3oooo3oxox *d3oooo&#xt → all heights = 1/sqrt(6) = 0.408248
(hex || pseudo hex-alt. trahex || pseudo {3}-dual trahex || hex-alt. hex)
o...3o... o...3o...3o... *d3o... & | 16 * ♦ 6 12 3 0 0 0 | 12 12 36 18 24 3 0 0 0 0 | 4 4 4 36 36 16 12 12 12 36 1 0 0 0 0 0 | 1 12 36 12 12 3 16 16 24 4 0 0 0 0 | 12 12 3 12 12 6 6 0 0 | 4 3 3 4
.o..3.o.. .o..3.o..3.o.. *d3.o.. & | * 48 ♦ 0 4 1 2 6 8 | 0 8 6 12 16 2 1 12 12 36 | 0 0 4 12 4 6 12 12 12 36 1 4 4 24 32 12 | 0 6 8 4 1 4 18 24 32 4 1 20 8 10 | 4 2 1 12 20 10 6 6 2 | 1 3 6 4
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x... .... .... .... & | 2 0 | 48 * * * * * ♦ 4 0 6 0 0 0 0 0 0 0 | 2 2 0 6 12 3 0 0 0 0 0 0 0 0 0 0 | 1 2 12 6 6 0 3 0 0 0 0 0 0 0 | 4 6 3 6 0 0 1 0 0 | 2 3 0 2
oo..3oo.. oo..3oo..3oo.. *d3oo..&#x & | 1 1 | * 192 * * * * ♦ 0 2 3 3 2 0 0 0 0 0 | 0 0 1 6 3 3 3 2 1 6 0 0 0 0 0 0 | 0 3 6 3 1 1 6 3 6 1 0 0 0 0 | 3 2 1 6 3 2 3 0 0 | 1 2 1 3
o.o.3o.o. o.o.3o.o.3o.o. *d3o.o.&#x & | 1 1 | * * 48 * * * ♦ 0 0 0 0 8 2 0 0 0 0 | 0 0 0 0 0 0 0 4 8 16 1 0 0 0 0 0 | 0 0 0 0 0 0 6 12 8 4 0 0 0 0 | 0 0 0 4 8 2 6 0 0 | 0 1 2 4
.x.. .... .... .... .... .... & | 0 2 | * * * 48 * * ♦ 0 4 0 0 0 1 1 0 4 0 | 0 0 4 6 0 0 0 4 4 0 1 0 0 6 0 0 | 0 6 4 0 0 0 6 6 0 4 0 4 0 0 | 4 1 0 4 4 0 6 1 0 | 1 1 1 4
.... .... .... .... .x.. .... & | 0 2 | * * * * 144 * ♦ 0 0 0 2 0 0 0 4 0 4 | 0 0 0 0 0 1 4 0 0 4 0 2 2 2 8 2 | 0 0 0 2 0 2 3 2 8 0 1 4 4 4 | 0 0 1 6 4 4 1 2 2 | 0 3 2 2
.oo.3.oo. .oo.3.oo.3.oo. *d3.oo.&#x | 0 2 | * * * * * 192 ♦ 0 0 0 0 2 0 0 0 2 6 | 0 0 0 0 0 0 0 2 2 6 0 0 0 6 6 3 | 0 0 0 0 0 0 6 6 6 1 0 6 3 2 | 0 0 0 6 6 2 3 2 1 | 0 2 2 3
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x...3o... .... .... & | 3 0 | 3 0 0 0 0 0 | 64 * * * * * * * * * | 1 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 | 1 0 3 3 3 0 0 0 0 0 0 0 0 0 | 1 3 3 3 0 0 0 0 0 | 1 3 0 1
ox.. .... .... .... .... ....&#x & | 1 2 | 0 2 0 1 0 0 | * 192 * * * * * * * * | 0 0 1 3 0 0 0 1 0 0 0 0 0 0 0 0 | 0 3 3 0 0 0 3 0 0 1 0 0 0 0 | 3 1 0 3 0 0 3 0 0 | 1 1 0 3
.... .... xo.. .... .... ....&#x & | 2 1 | 1 2 0 0 0 0 | * * 288 * * * * * * * | 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 | 0 1 4 2 1 0 2 0 0 0 0 0 0 0 | 2 2 1 4 0 0 1 0 0 | 1 2 0 2
.... .... .... .... ox.. ....&#x & | 1 2 | 0 2 0 0 1 0 | * * * 288 * * * * * * | 0 0 0 0 0 1 2 0 0 2 0 0 0 0 0 0 | 0 0 0 2 0 1 2 1 4 0 0 0 0 0 | 0 0 1 4 2 2 1 0 0 | 0 2 1 2
ooo.3ooo. ooo.3ooo.3ooo. *d3ooo.&#x & | 1 2 | 0 1 1 0 0 1 | * * * * 384 * * * * * | 0 0 0 0 0 0 0 1 1 3 0 0 0 0 0 0 | 0 0 0 0 0 0 3 3 3 1 0 0 0 0 | 0 0 0 3 3 1 3 0 0 | 0 1 1 3
.... o.x. .... .... .... ....&#x & | 1 2 | 0 0 2 1 0 0 | * * * * * 48 * * * * | 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 | 0 0 0 0 0 0 0 6 0 4 0 0 0 0 | 0 0 0 0 4 0 6 0 0 | 0 0 1 4
.x..3.o.. .... .... .... .... & | 0 3 | 0 0 0 3 0 0 | * * * * * * 16 * * * | 0 0 4 0 0 0 0 0 0 0 1 0 0 0 0 0 | 0 6 0 0 0 0 0 0 0 4 0 0 0 0 | 4 0 0 0 0 0 6 0 0 | 1 0 0 4
.... .... .... .o..3.x.. .... & | 0 3 | 0 0 0 0 3 0 | * * * * * * * 192 * * | 0 0 0 0 0 0 1 0 0 0 0 1 1 0 2 0 | 0 0 0 1 0 1 0 0 2 0 1 1 2 2 | 0 0 1 3 1 2 0 1 2 | 0 3 1 1
.xo. .... .... .... .... ....&#x & | 0 3 | 0 0 0 1 0 2 | * * * * * * * * 192 * | 0 0 0 0 0 0 0 1 1 0 0 0 0 3 0 0 | 0 0 0 0 0 0 3 3 0 1 0 3 0 0 | 0 0 0 3 3 0 3 1 0 | 0 1 1 3
.... .... .ox. .... .... ....&#x & | 0 3 | 0 0 0 0 1 2 | * * * * * * * * * 576 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 2 1 | 0 0 0 0 0 0 2 1 2 0 0 2 2 1 | 0 0 0 4 2 1 1 1 1 | 0 2 1 2
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x...3o...3o... .... & ♦ 4 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * * * * * * * ♦ 1 0 0 3 0 0 0 0 0 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 | 0 3 0 1
.... .... x...3o... .... *d3o... & ♦ 4 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | * 16 * * * * * * * * * * * * * * | 1 0 0 0 3 0 0 0 0 0 0 0 0 0 | 0 3 3 0 0 0 0 0 0 | 1 3 0 0
ox..3oo.. .... .... .... ....&#x & ♦ 1 3 | 0 3 0 3 0 0 | 0 3 0 0 0 0 1 0 0 0 | * * 64 * * * * * * * * * * * * * | 0 3 0 0 0 0 0 0 0 1 0 0 0 0 | 3 0 0 0 0 0 3 0 0 | 1 0 0 3
ox.. .... xo.. .... .... ....&#x & ♦ 2 2 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 0 0 0 | * * * 288 * * * * * * * * * * * * | 0 1 2 0 0 0 1 0 0 0 0 0 0 0 | 2 1 0 2 0 0 1 0 0 | 1 1 0 2
.... .... xo..3oo.. .... ....&#x & ♦ 3 1 | 3 3 0 0 0 0 | 1 0 3 0 0 0 0 0 0 0 | * * * * 192 * * * * * * * * * * * | 0 0 2 1 1 0 0 0 0 0 0 0 0 0 | 1 2 1 2 0 0 0 0 0 | 1 2 0 1
.... .... xo.. .... ox.. ....&#x & ♦ 2 2 | 1 4 0 0 1 0 | 0 0 2 2 0 0 0 0 0 0 | * * * * * 144 * * * * * * * * * * ♦ 0 0 0 2 0 0 2 0 0 0 0 0 0 0 | 0 0 1 4 0 0 1 0 0 | 0 2 0 2
.... .... .... oo..3ox.. ....&#x & ♦ 1 3 | 0 3 0 0 3 0 | 0 0 0 3 0 0 0 1 0 0 | * * * * * * 192 * * * * * * * * * | 0 0 0 1 0 1 0 0 2 0 0 0 0 0 | 0 0 1 2 1 2 0 0 0 | 0 2 1 1
oxo. .... .... .... .... ....&#x & ♦ 1 3 | 0 2 1 1 0 2 | 0 1 0 0 2 0 0 0 1 0 | * * * * * * * 192 * * * * * * * * ♦ 0 0 0 0 0 0 3 0 0 1 0 0 0 0 | 0 0 0 3 0 0 3 0 0 | 0 1 0 3
.... oox. .... .... .... ....&#x & ♦ 1 3 | 0 1 2 1 0 2 | 0 0 0 0 2 1 0 0 1 0 | * * * * * * * * 192 * * * * * * * | 0 0 0 0 0 0 0 3 0 1 0 0 0 0 | 0 0 0 0 3 0 3 0 0 | 0 0 1 3
.... .... .... .... oxo. ....&#x & ♦ 1 3 | 0 2 1 0 1 2 | 0 0 0 1 2 0 0 0 0 1 | * * * * * * * * * 576 * * * * * * | 0 0 0 0 0 0 1 1 2 0 0 0 0 0 | 0 0 0 2 2 1 1 0 0 | 0 1 1 2
o.o.3o.x. .... .... .... ....&#x & ♦ 1 3 | 0 0 3 3 0 0 | 0 0 0 0 0 3 1 0 0 0 | * * * * * * * * * * 16 * * * * * ♦ 0 0 0 0 0 0 0 0 0 4 0 0 0 0 | 0 0 0 0 0 0 6 0 0 | 0 0 0 4
.... .... .o..3.o..3.x.. .... & ♦ 0 4 | 0 0 0 0 6 0 | 0 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * * 48 * * * * ♦ 0 0 0 1 0 0 0 0 0 0 1 0 2 0 | 0 0 1 3 0 0 0 0 2 | 0 3 0 1
.... .... .... .o..3.x.. *d3.o.. & ♦ 0 4 | 0 0 0 0 6 0 | 0 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * * * 48 * * * | 0 0 0 0 0 1 0 0 0 0 1 0 0 2 | 0 0 1 0 0 2 0 1 2 | 0 3 1 0
.xo. .... .ox. .... .... ....&#x & ♦ 0 4 | 0 0 0 1 1 4 | 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * 288 * * | 0 0 0 0 0 0 1 1 0 0 0 2 0 0 | 0 0 0 2 2 0 1 1 0 | 0 1 1 2
.... .... .ox.3.oo. .... ....&#x & ♦ 0 4 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 1 0 3 | * * * * * * * * * * * * * * 384 * | 0 0 0 0 0 0 0 0 1 0 0 1 1 1 | 0 0 0 2 1 1 0 1 1 | 0 2 1 1
.... .... .ox. .... .xo. ....&#x ♦ 0 4 | 0 0 0 0 2 4 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * 144 ♦ 0 0 0 0 0 0 2 0 0 0 0 0 2 0 | 0 0 0 4 0 0 1 0 1 | 0 2 0 2
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x...3o...3o... *d3o... & ♦ 8 0 | 24 0 0 0 0 0 | 32 0 0 0 0 0 0 0 0 0 | 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * | 0 0 3 0 0 0 0 0 0 | 0 3 0 0
ox..3oo.. xo.. .... .... ....&#x & ♦ 2 3 | 1 6 0 3 0 0 | 0 6 3 0 0 0 1 0 0 0 | 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 | * 96 * * * * * * * * * * * * | 2 0 0 0 0 0 1 0 0 | 1 0 0 2
ox.. .... xo..3oo.. .... ....&#x & ♦ 3 2 | 3 6 0 1 0 0 | 1 3 6 0 0 0 0 0 0 0 | 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 | * * 192 * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 0 1
.... .... xo..3oo..3ox.. ....&#x & ♦ 4 4 | 6 12 0 0 6 0 | 4 0 12 12 0 0 0 4 0 0 | 1 0 0 0 4 6 4 0 0 0 0 1 0 0 0 0 | * * * 48 * * * * * * * * * * | 0 0 1 2 0 0 0 0 0 | 0 2 0 1
.... .... xo..3oo.. .... *d3oo..&#x & ♦ 4 1 | 6 4 0 0 0 0 | 4 0 6 0 0 0 0 0 0 0 | 0 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 | * * * * 48 * * * * * * * * * | 0 2 1 0 0 0 0 0 0 | 1 2 0 0
.... .... .... oo..3ox.. *d3oo..&#x & ♦ 1 4 | 0 4 0 0 6 0 | 0 0 0 6 0 0 0 4 0 0 | 0 0 0 0 0 0 4 0 0 0 0 0 1 0 0 0 | * * * * * 48 * * * * * * * * | 0 0 1 0 0 2 0 0 0 | 0 2 1 0
oxo. .... xox. .... oxo. ....&#xt & ♦ 2 6 | 1 8 2 2 3 8 | 0 4 4 4 8 0 0 0 4 8 | 0 0 0 2 0 2 0 4 0 4 0 0 0 2 0 2 | * * * * * * 144 * * * * * * * | 0 0 0 2 0 0 1 0 0 | 0 1 0 2
.... oox. .... .... oxo. ....&#x & ♦ 1 4 | 0 2 2 1 1 4 | 0 0 0 1 4 1 0 0 2 2 | 0 0 0 0 0 0 0 0 2 2 0 0 0 1 0 0 | * * * * * * * 288 * * * * * * | 0 0 0 0 2 0 1 0 0 | 0 0 1 2
.... .... .... ooo.3oxo. ....&#x & ♦ 1 4 | 0 3 1 0 3 3 | 0 0 0 3 3 0 0 1 0 3 | 0 0 0 0 0 0 1 0 0 3 0 0 0 0 1 0 | * * * * * * * * 384 * * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1
oxoo3ooxo .... .... .... ....&#xr ♦ 2 6 | 0 6 6 6 0 6 | 0 6 0 0 12 6 2 0 6 0 | 0 0 2 0 0 0 0 6 6 0 2 0 0 0 0 0 | * * * * * * * * * 32 * * * * | 0 0 0 0 0 0 3 0 0 | 0 0 0 3 cycle: (ABDC)
.... .... .o..3.o..3.x.. *d3.o.. & ♦ 0 8 | 0 0 0 0 24 0 | 0 0 0 0 0 0 0 32 0 0 | 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 | * * * * * * * * * * 6 * * * | 0 0 1 0 0 0 0 0 2 | 0 3 0 0
.xo. .... .ox.3.oo. .... ....&#x & ♦ 0 5 | 0 0 0 1 3 6 | 0 0 0 0 0 0 0 1 3 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 | * * * * * * * * * * * 192 * * | 0 0 0 1 1 0 0 1 0 | 0 1 1 1
.... .... .ox.3.oo.3.xo. ....&#x ♦ 0 8 | 0 0 0 0 12 12 | 0 0 0 0 0 0 0 8 0 24 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 8 6 | * * * * * * * * * * * * 48 * | 0 0 0 2 0 0 0 0 1 | 0 2 0 1
.... .... .ox.3.oo. .... *d3.oo.&#x & ♦ 0 5 | 0 0 0 0 6 4 | 0 0 0 0 0 0 0 4 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 | * * * * * * * * * * * * * 96 | 0 0 0 0 0 1 0 1 1 | 0 2 1 0
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
ox..3oo.. xo..3oo.. .... ....&#x & ♦ 3 3 | 3 9 0 3 0 0 | 1 9 9 0 0 0 1 0 0 0 | 0 0 3 9 3 0 0 0 0 0 0 0 0 0 0 0 | 0 3 3 0 0 0 0 0 0 0 0 0 0 0 | 64 * * * * * * * * | 1 0 0 1
ox.. .... xo..3oo.. .... *d3oo..&#x & ♦ 4 2 | 6 8 0 1 0 0 | 4 4 12 0 0 0 0 0 0 0 | 0 1 0 6 8 0 0 0 0 0 0 0 0 0 0 0 | 0 0 4 0 2 0 0 0 0 0 0 0 0 0 | * 48 * * * * * * * | 1 1 0 0
.... .... xo..3oo..3ox.. *d3oo..&#x & ♦ 8 8 | 24 32 0 0 24 0 | 32 0 48 48 0 0 0 32 0 0 | 8 8 0 0 32 24 32 0 0 0 0 8 8 0 0 0 | 1 0 0 8 8 8 0 0 0 0 1 0 0 0 | * * 6 * * * * * * | 0 2 0 0
oxo. .... xox.3ooo.3oxo. ....&#xt & ♦ 4 12 | 6 24 4 4 18 24 | 4 12 24 24 24 0 0 12 12 48 | 1 0 0 12 8 12 8 12 0 24 0 3 0 12 16 12 | 0 0 4 2 0 0 6 0 8 0 0 4 2 0 | * * * 48 * * * * * | 0 1 0 1
.... oox. .... ooo.3oxo. ....&#xt & ♦ 1 5 | 0 3 2 1 3 6 | 0 0 0 3 6 1 0 1 3 6 | 0 0 0 0 0 0 1 0 3 6 0 0 0 3 2 0 | 0 0 0 0 0 0 0 3 2 0 0 1 0 0 | * * * * 192 * * * * | 0 0 1 1
.... .... .... ooo.3oxo. *d3ooo.&#x & ♦ 1 5 | 0 4 1 0 6 4 | 0 0 0 6 4 0 0 4 0 6 | 0 0 0 0 0 0 4 0 0 6 0 0 1 0 4 0 | 0 0 0 0 0 1 0 0 4 0 0 0 0 1 | * * * * * 96 * * * | 0 1 1 0
oxoo3ooxo xoxo .... oxox ....&#xt & ♦ 4 12 | 2 24 12 12 6 24 | 0 24 12 12 48 12 4 0 24 24 | 0 0 8 12 0 6 0 24 24 24 4 0 0 12 0 6 | 0 4 0 0 0 0 6 12 0 4 0 0 0 0 | * * * * * * 24 * * | 0 0 0 2
.xo. .... .ox.3.oo. .... *d3.oo.&#x & ♦ 0 6 | 0 0 0 1 6 8 | 0 0 0 0 0 0 0 4 4 12 | 0 0 0 0 0 0 0 0 0 0 0 0 1 6 8 0 | 0 0 0 0 0 0 0 0 0 0 0 4 0 2 | * * * * * * * 48 * | 0 1 1 0
.... .... .ox.3.oo.3.xo. *d3.oo.&#x ♦ 0 16 | 0 0 0 0 48 32 | 0 0 0 0 0 0 0 64 0 96 | 0 0 0 0 0 0 0 0 0 0 0 16 16 0 64 24 | 0 0 0 0 0 0 0 0 0 0 2 0 8 16 | * * * * * * * * 6 | 0 2 0 0
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
ox..3oo.. xo..3oo.. .... *d3oo..&#x & ♦ 4 3 | 6 12 0 3 0 0 | 4 12 18 0 0 0 1 0 0 0 | 0 1 4 18 12 0 0 0 0 0 0 0 0 0 0 0 | 0 6 12 0 3 0 0 0 0 0 0 0 0 0 | 4 3 0 0 0 0 0 0 0 | 16 * * *
oxo. .... xox.3ooo.3oxo. *d3ooo.&#xt & ♦ 8 24 | 24 64 8 8 72 64 | 32 32 96 96 64 0 0 96 32 192 | 8 8 0 48 64 48 64 32 0 96 0 24 24 48 128 48 | 1 0 32 16 16 16 24 0 64 0 3 32 16 32 | 0 8 2 8 0 16 0 8 2 | * 6 * *
.... oox. .... ooo.3oxo. *d3ooo.&#x & ♦ 1 6 | 0 4 2 1 6 8 | 0 0 0 6 8 1 0 4 4 12 | 0 0 0 0 0 0 4 0 4 12 0 0 1 6 8 0 | 0 0 0 0 0 1 0 6 8 0 0 4 0 2 | 0 0 0 0 4 2 0 1 0 | * * 48 *
oxoo3ooxo xoxo3oooo3oxox ....&#xt ♦ 8 24 | 12 72 24 24 36 72 | 8 72 72 72 144 24 8 24 72 144 | 2 0 24 72 24 36 24 72 72 144 8 6 0 72 48 36 | 0 24 24 6 0 0 36 72 48 12 0 24 6 0 | 8 0 0 6 24 0 6 0 0 | * * * 8
xo3oo3ox *b3oo xo3oo3ox&#zx → height = 0
(tegum sum of 2 mutually gyro-dual tethexes)
o.3o.3o. *b3o. o.3o.3o. & | 64 ♦ 6 3 12 | 12 3 54 36 | 4 4 1 48 18 72 16 12 | 1 12 15 60 18 30 4 | 3 12 18 24 6 | 3 4 7
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x. .. .. .. .. .. .. & | 2 | 192 * * ♦ 4 0 6 0 | 2 2 0 12 3 6 0 0 | 1 6 6 12 3 2 0 | 3 6 6 4 1 | 3 2 2
.. .. .. .. x. .. .. & | 2 | * 96 * ♦ 0 2 0 8 | 0 0 1 0 0 12 8 4 | 0 0 0 8 6 12 4 | 0 4 2 8 6 | 1 4 2
oo3oo3oo *b3oo oo3oo3oo&#x | 2 | * * 384 ♦ 0 0 6 4 | 0 0 0 6 3 12 2 2 | 0 3 2 12 6 6 1 | 1 6 4 6 3 | 2 3 2
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x.3o. .. .. .. .. .. & | 3 | 3 0 0 | 256 * * * | 1 1 0 3 0 0 0 0 | 1 3 3 3 0 0 0 | 3 3 3 1 0 | 3 1 1
.. .. .. .. x.3o.... & | 3 | 0 3 0 | * 64 * * | 0 0 1 0 0 0 4 0 | 0 0 0 0 0 6 4 | 0 0 0 4 6 | 0 4 1
xo .. .. .. .. .. ..&#x & | 3 | 1 0 2 | * * 1152 * | 0 0 0 2 1 2 0 0 | 0 2 1 4 2 1 0 | 1 4 2 2 1 | 2 2 1
.. .. .. .. xo .. ..&#x & | 3 | 0 1 2 | * * * 768 | 0 0 0 0 0 3 1 1 | 0 0 0 3 3 3 1 | 0 3 1 3 3 | 1 3 1
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x.3o.3o. .. .. .. .. & ♦ 4 | 6 0 0 | 4 0 0 0 | 64 * * * * * * * ♦ 1 3 0 0 0 0 0 | 3 3 0 0 0 | 3 1 0
x.3o. .. *b3o. .. .. .. & ♦ 4 | 6 0 0 | 4 0 0 0 | * 64 * * * * * * | 1 0 3 0 0 0 0 | 3 0 3 0 0 | 3 0 1
.. .. .. .. x.3o.3o. & ♦ 4 | 0 6 0 | 0 4 0 0 | * * 16 * * * * * ♦ 0 0 0 0 0 0 4 | 0 0 0 0 6 | 0 4 0
xo3oo .. .. .. .. ..&#x & ♦ 4 | 3 0 3 | 1 0 3 0 | * * * 768 * * * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 | 2 1 1
xo .. ox .. .. .. ..&#x ♦ 4 | 2 0 4 | 0 0 4 0 | * * * * 288 * * * ♦ 0 2 0 0 2 0 0 | 1 4 0 0 1 | 2 2 0
xo .. .. .. .. .. ox&#x & ♦ 4 | 1 1 4 | 0 0 2 2 | * * * * * 1152 * * | 0 0 0 2 1 1 0 | 0 2 1 2 1 | 1 2 1
.. .. .. .. xo3oo ..&#x & ♦ 4 | 0 3 3 | 0 1 0 3 | * * * * * * 256 * | 0 0 0 0 0 3 1 | 0 0 0 3 3 | 0 3 1
.. .. .. .. xo .. ox&#x ♦ 4 | 0 2 4 | 0 0 0 4 | * * * * * * * 192 ♦ 0 0 0 0 3 0 1 | 0 3 0 0 3 | 1 3 0
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x.3o.3o. *b3o. .. .. .. & ♦ 8 | 24 0 0 | 32 0 0 0 | 8 8 0 0 0 0 0 0 | 8 * * * * * * | 3 0 0 0 0 | 3 0 0
xo3oo3ox .. .. .. ..&#x ♦ 8 | 12 0 12 | 8 0 24 0 | 2 0 0 8 6 0 0 0 | * 96 * * * * * | 1 2 0 0 0 | 2 1 0
xo3oo .. *b3oo .. .. ..&#x & ♦ 5 | 6 0 4 | 4 0 6 0 | 0 1 0 4 0 0 0 0 | * * 192 * * * * | 1 0 2 0 0 | 2 0 1
xo3oo .. .. .. .. ox&#x & ♦ 5 | 3 1 6 | 1 0 6 3 | 0 0 0 2 0 3 0 0 | * * * 768 * * * | 0 1 1 1 0 | 1 1 1
xo .. ox .. xo .. ox&#zx ♦ 8 | 4 4 16 | 0 0 16 16 | 0 0 0 0 4 8 0 4 | * * * * 144 * * | 0 2 0 0 1 | 1 2 0
xo .. .. .. .. oo3ox&#x & ♦ 5 | 1 3 6 | 0 1 3 6 | 0 0 0 0 0 3 2 0 | * * * * * 384 * | 0 0 0 2 1 | 0 2 1
.. .. .. .. xo3oo3ox&#x ♦ 8 | 0 12 12 | 0 8 0 24 | 0 0 2 0 0 0 8 6 | * * * * * * 32 | 0 0 0 0 3 | 0 3 0
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
xo3oo3ox *b3oo .. .. ..&#x ♦ 16 | 48 0 32 | 64 0 96 0 | 16 16 0 64 24 0 0 0 | 2 8 16 0 0 0 0 | 12 * * * * | 2 0 0
xo3oo3ox .. xo .. ox&#zx ♦ 16 | 24 8 48 | 16 0 96 48 | 4 0 0 32 24 48 0 12 | 0 4 0 16 6 0 0 | * 48 * * * | 1 1 0
xo3oo .. *b3oo .. .. ox&#x & ♦ 6 | 6 1 8 | 4 0 12 4 | 0 1 0 8 0 6 0 0 | 0 0 2 4 0 0 0 | * * 192 * * | 1 0 1
xo3oo .. .. .. oo3ox&#x & ♦ 6 | 3 3 9 | 1 1 9 9 | 0 0 0 3 0 9 3 0 | 0 0 0 3 0 3 0 | * * * 256 * | 0 1 1
xo .. ox .. xo3oo3ox&#zx ♦ 16 | 8 24 48 | 0 16 48 96 | 0 0 4 0 12 48 32 24 | 0 0 0 0 6 16 4 | * * * * 24 | 0 2 0
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
xo3oo3ox *b3oo xo .. ox&#zx ♦ 32 | 96 16 128 | 128 0 384 128 | 32 32 0 256 96 192 0 32 | 4 32 64 128 24 0 0 | 4 8 32 0 0 | 6 * *
xo3oo3ox .. xo3oo3ox&#zx ♦ 32 | 48 48 144 | 32 32 288 288 | 8 0 8 96 72 288 96 72 | 0 12 0 96 36 96 12 | 0 6 0 32 6 | * 8 *
xo3oo .. *b3oo .. oo3ox&#x & ♦ 7 | 6 3 12 | 4 1 18 12 | 0 1 0 12 0 18 4 0 | 0 0 3 12 0 6 0 | 0 0 3 4 0 | * * 64