hix

Acronym hix

Name hexateron,
5D simplex (α₅),
pyropet(id),
pentachoral pyramid,
regular tet-scalene,
regular triangle-tettene,
regular line-pennene,
regular (point-)hixene,
digonal gyrotrigonism,
vertex figure of hop,
Gosset polytope 0₄

|,>,O device line pyramid pyramid pyramid pyramid = |>>>>

Field of sections

©

Circumradius sqrt(5/12) = 0.645497

Inradius 1/sqrt(60) = 0.129099

Vertex figure

 ©    ©

Lace city
in approx. ASCII-art

o3o3o   o3o3o
             
             
    x3o3o

    x o o    
             
             
             
             
o x o   o o x

Lace hyper city
in approx. ASCII-art

©

x3o

{3}

perp {3}

Volume sqrt(3)/480 = 0.0036084

Surface sqrt(5)/16 = 0.139754

Rel. Roundness 8 π² sqrt(5)/3375 = 5.231196 %

Dual (selfdual, in different orientation)

Dihedral angles

at tet between pen and pen: arccos(1/5) = 78.463041°

Face vector 6, 15, 20, 15, 6

Confer

more general:: {n/d} || perp {n/d}
related segmentotera:: pexhix pabex hix
compounds:: stade
ambification:: rix
general polytopal classes:: Wythoffian polytera simplex scalene tettene pennene noble polytopes partial Stott expansions segmentotera fundamental lace prisms lace simplices Coxeter-Elte-Gosset polytopes
analogs:: regular simplex S_n

External
links

Incidence matrix according to Dynkin symbol

x3o3o3o3o

. . . . . | 6 ♦  5 | 10 | 10 | 5
----------+---+----+----+----+--
x . . . . | 2 | 15 ♦  4 |  6 | 4
----------+---+----+----+----+--
x3o . . . | 3 |  3 | 20 |  3 | 3
----------+---+----+----+----+--
x3o3o . . ♦ 4 |  6 |  4 | 15 | 2
----------+---+----+----+----+--
x3o3o3o . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3o3o3o

.   . . . . | 6 ♦  5 | 10 | 10 | 5
------------+---+----+----+----+--
x   . . . . | 2 | 15 ♦  4 |  6 | 4
------------+---+----+----+----+--
x3/2o . . . | 3 |  3 | 20 |  3 | 3
------------+---+----+----+----+--
x3/2o3o . . ♦ 4 |  6 |  4 | 15 | 2
------------+---+----+----+----+--
x3/2o3o3o . ♦ 5 | 10 | 10 |  5 | 6

x3o3/2o3o3o

. .   . . . | 6 ♦  5 | 10 | 10 | 5
------------+---+----+----+----+--
x .   . . . | 2 | 15 ♦  4 |  6 | 4
------------+---+----+----+----+--
x3o   . . . | 3 |  3 | 20 |  3 | 3
------------+---+----+----+----+--
x3o3/2o . . ♦ 4 |  6 |  4 | 15 | 2
------------+---+----+----+----+--
x3o3/2o3o . ♦ 5 | 10 | 10 |  5 | 6

x3o3o3/2o3o

. . .   . . | 6 ♦  5 | 10 | 10 | 5
------------+---+----+----+----+--
x . .   . . | 2 | 15 ♦  4 |  6 | 4
------------+---+----+----+----+--
x3o .   . . | 3 |  3 | 20 |  3 | 3
------------+---+----+----+----+--
x3o3o   . . ♦ 4 |  6 |  4 | 15 | 2
------------+---+----+----+----+--
x3o3o3/2o . ♦ 5 | 10 | 10 |  5 | 6

x3o3o3o3/2o

. . . .   . | 6 ♦  5 | 10 | 10 | 5
------------+---+----+----+----+--
x . . .   . | 2 | 15 ♦  4 |  6 | 4
------------+---+----+----+----+--
x3o . .   . | 3 |  3 | 20 |  3 | 3
------------+---+----+----+----+--
x3o3o .   . ♦ 4 |  6 |  4 | 15 | 2
------------+---+----+----+----+--
x3o3o3o   . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3/2o3o3o

.   .   . . . | 6 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+--
x   .   . . . | 2 | 15 ♦  4 |  6 | 4
--------------+---+----+----+----+--
x3/2o   . . . | 3 |  3 | 20 |  3 | 3
--------------+---+----+----+----+--
x3/2o3/2o . . ♦ 4 |  6 |  4 | 15 | 2
--------------+---+----+----+----+--
x3/2o3/2o3o . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3o3/2o3o

.   . .   . . | 6 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+--
x   . .   . . | 2 | 15 ♦  4 |  6 | 4
--------------+---+----+----+----+--
x3/2o .   . . | 3 |  3 | 20 |  3 | 3
--------------+---+----+----+----+--
x3/2o3o   . . ♦ 4 |  6 |  4 | 15 | 2
--------------+---+----+----+----+--
x3/2o3o3/2o . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3o3o3/2o

.   . . .   . | 6 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+--
x   . . .   . | 2 | 15 ♦  4 |  6 | 4
--------------+---+----+----+----+--
x3/2o . .   . | 3 |  3 | 20 |  3 | 3
--------------+---+----+----+----+--
x3/2o3o .   . ♦ 4 |  6 |  4 | 15 | 2
--------------+---+----+----+----+--
x3/2o3o3o   . ♦ 5 | 10 | 10 |  5 | 6

x3o3/2o3/2o3o

. .   .   . . | 6 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+--
x .   .   . . | 2 | 15 ♦  4 |  6 | 4
--------------+---+----+----+----+--
x3o   .   . . | 3 |  3 | 20 |  3 | 3
--------------+---+----+----+----+--
x3o3/2o   . . ♦ 4 |  6 |  4 | 15 | 2
--------------+---+----+----+----+--
x3o3/2o3/2o . ♦ 5 | 10 | 10 |  5 | 6

x3o3/2o3o3/2o

. .   . .   . | 6 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+--
x .   . .   . | 2 | 15 ♦  4 |  6 | 4
--------------+---+----+----+----+--
x3o   . .   . | 3 |  3 | 20 |  3 | 3
--------------+---+----+----+----+--
x3o3/2o .   . ♦ 4 |  6 |  4 | 15 | 2
--------------+---+----+----+----+--
x3o3/2o3o   . ♦ 5 | 10 | 10 |  5 | 6

x3o3o3/2o3/2o

. . .   .   . | 6 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+--
x . .   .   . | 2 | 15 ♦  4 |  6 | 4
--------------+---+----+----+----+--
x3o .   .   . | 3 |  3 | 20 |  3 | 3
--------------+---+----+----+----+--
x3o3o   .   . ♦ 4 |  6 |  4 | 15 | 2
--------------+---+----+----+----+--
x3o3o3/2o   . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3/2o3/2o3o

.   .   .   . . | 6 ♦  5 | 10 | 10 | 5
----------------+---+----+----+----+--
x   .   .   . . | 2 | 15 ♦  4 |  6 | 4
----------------+---+----+----+----+--
x3/2o   .   . . | 3 |  3 | 20 |  3 | 3
----------------+---+----+----+----+--
x3/2o3/2o   . . ♦ 4 |  6 |  4 | 15 | 2
----------------+---+----+----+----+--
x3/2o3/2o3/2o . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3/2o3o3/2o

.   .   . .   . | 6 ♦  5 | 10 | 10 | 5
----------------+---+----+----+----+--
x   .   . .   . | 2 | 15 ♦  4 |  6 | 4
----------------+---+----+----+----+--
x3/2o   . .   . | 3 |  3 | 20 |  3 | 3
----------------+---+----+----+----+--
x3/2o3/2o .   . ♦ 4 |  6 |  4 | 15 | 2
----------------+---+----+----+----+--
x3/2o3/2o3o   . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3o3/2o3/2o

.   . .   .   . | 6 ♦  5 | 10 | 10 | 5
----------------+---+----+----+----+--
x   . .   .   . | 2 | 15 ♦  4 |  6 | 4
----------------+---+----+----+----+--
x3/2o .   .   . | 3 |  3 | 20 |  3 | 3
----------------+---+----+----+----+--
x3/2o3o   .   . ♦ 4 |  6 |  4 | 15 | 2
----------------+---+----+----+----+--
x3/2o3o3/2o   . ♦ 5 | 10 | 10 |  5 | 6

x3o3/2o3/2o3/2o

. .   .   .   . | 6 ♦  5 | 10 | 10 | 5
----------------+---+----+----+----+--
x .   .   .   . | 2 | 15 ♦  4 |  6 | 4
----------------+---+----+----+----+--
x3o   .   .   . | 3 |  3 | 20 |  3 | 3
----------------+---+----+----+----+--
x3o3/2o   .   . ♦ 4 |  6 |  4 | 15 | 2
----------------+---+----+----+----+--
x3o3/2o3/2o   . ♦ 5 | 10 | 10 |  5 | 6

x3/2o3/2o3/2o3/2o

.   .   .   .   . | 6 ♦  5 | 10 | 10 | 5
------------------+---+----+----+----+--
x   .   .   .   . | 2 | 15 ♦  4 |  6 | 4
------------------+---+----+----+----+--
x3/2o   .   .   . | 3 |  3 | 20 |  3 | 3
------------------+---+----+----+----+--
x3/2o3/2o   .   . ♦ 4 |  6 |  4 | 15 | 2
------------------+---+----+----+----+--
x3/2o3/2o3/2o   . ♦ 5 | 10 | 10 |  5 | 6

ox3oo3oo3oo&#x   → height = sqrt(3/5) = 0.774597
(pt || pen)

o.3o.3o.3o.    | 1 * ♦ 5  0 | 10  0 | 10 0 | 5 0
.o3.o3.o3.o    | * 5 ♦ 1  4 |  4  6 |  6 4 | 4 1
---------------+-----+------+-------+------+----
oo3oo3oo3oo&#x | 1 1 | 5  * ♦  4  0 |  6 0 | 4 0
.x .. .. ..    | 0 2 | * 10 ♦  1  3 |  3 3 | 3 1
---------------+-----+------+-------+------+----
ox .. .. ..&#x | 1 2 | 2  1 | 10  * |  3 0 | 3 0
.x3.o .. ..    | 0 3 | 0  3 |  * 10 |  1 2 | 2 1
---------------+-----+------+-------+------+----
ox3oo .. ..&#x ♦ 1 3 | 3  3 |  3  1 | 10 * | 2 0
.x3.o3.o ..    ♦ 0 4 | 0  6 |  0  4 |  * 5 | 1 1
---------------+-----+------+-------+------+----
ox3oo3oo ..&#x ♦ 1 4 | 4  6 |  6  4 |  4 1 | 5 *
.x3.o3.o3.o    ♦ 0 5 | 0 10 |  0 10 |  0 5 | * 1

xo ox3oo3oo&#x   → height = sqrt(3/8) = 0.612372
(line || perp tet)

o. o.3o.3o.    | 2 * ♦ 1 4 0 | 4  6 0 | 6 4 0 | 4 1
.o .o3.o3.o    | * 4 ♦ 0 2 3 | 1  6 3 | 3 6 1 | 3 2
---------------+-----+-------+--------+-------+----
x. .. .. ..    | 2 0 | 1 * * ♦ 4  0 0 | 6 0 0 | 4 0
oo oo3oo3oo&#x | 1 1 | * 8 * ♦ 1  3 0 | 3 3 0 | 3 1
.. .x .. ..    | 0 2 | * * 6 ♦ 0  2 2 | 1 4 1 | 2 2
---------------+-----+-------+--------+-------+----
xo .. .. ..&#x | 2 1 | 1 2 0 | 4  * * | 3 0 0 | 3 0
.. ox .. ..&#x | 1 2 | 0 2 1 | * 12 * | 1 2 0 | 2 1
.. .x3.o ..    | 0 3 | 0 0 3 | *  * 4 | 0 2 1 | 1 2
---------------+-----+-------+--------+-------+----
xo ox .. ..&#x ♦ 2 2 | 1 4 1 | 2  2 0 | 6 * * | 2 0
.. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0  3 1 | * 8 * | 1 1
.. .x3.o3.o    ♦ 0 4 | 0 0 6 | 0  0 4 | * * 1 | 0 2
---------------+-----+-------+--------+-------+----
xo ox3oo ..&#x ♦ 2 3 | 1 6 3 | 3  6 1 | 3 2 0 | 4 *
.. ox3oo3oo&#x ♦ 1 4 | 0 4 6 | 0  6 4 | 0 4 1 | * 2

xo3oo ox3oo&#x   → height = 1/sqrt(3) = 0.577350
({3} || perp {3})

o.3o. o.3o.    | 3 * ♦ 2 3 0 | 1 6 3 0 | 3 6 1 | 3 2
.o3.o .o3.o    | * 3 ♦ 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3
---------------+-----+-------+---------+-------+----
x. .. .. ..    | 2 0 | 3 * * ♦ 1 3 0 0 | 3 3 0 | 3 1
oo3oo oo3oo&#x | 1 1 | * 9 * ♦ 0 2 2 0 | 1 4 1 | 2 2
.. .. .x ..    | 0 2 | * * 3 ♦ 0 0 3 1 | 0 3 3 | 1 3
---------------+-----+-------+---------+-------+----
x.3o. .. ..    | 3 0 | 3 0 0 | 1 * * * | 3 0 0 | 3 0
xo .. .. ..&#x | 2 1 | 1 2 0 | * 9 * * | 1 2 0 | 2 1
.. .. ox ..&#x | 1 2 | 0 2 1 | * * 9 * | 0 2 1 | 1 2
.. .. .x3.o    | 0 3 | 0 0 3 | * * * 1 | 0 0 3 | 0 3
---------------+-----+-------+---------+-------+----
xo3oo .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | 3 * * | 2 0
xo .. ox ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * 9 * | 1 1
.. .. ox3oo&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * 3 | 0 2
---------------+-----+-------+---------+-------+----
xo3oo ox ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 2 3 0 | 3 *
xo .. ox3oo&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 3 2 | * 3

or
o.3o. o.3o.    & | 6 ♦ 2 3 | 1  9 | 4 3 | 5
-----------------+---+-----+------+-----+--
x. .. .. ..    & | 2 | 6 * ♦ 1  3 | 3 3 | 4
oo3oo oo3oo&#x   | 2 | * 9 ♦ 0  4 | 2 4 | 4
-----------------+---+-----+------+-----+--
x.3o. .. ..    & | 3 | 3 0 | 2  * | 3 0 | 3
xo .. .. ..&#x & | 3 | 1 2 | * 18 | 1 2 | 3
-----------------+---+-----+------+-----+--
xo3oo .. ..&#x & ♦ 4 | 3 3 | 1  3 | 6 * | 2
xo .. ox ..&#x   ♦ 4 | 2 4 | 0  4 | * 9 | 2
-----------------+---+-----+------+-----+--
xo3oo ox ..&#x & ♦ 5 | 4 6 | 1  9 | 2 3 | 6

oxo3ooo3ooo&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = 1
( (pt || tet) || pt )

o..3o..3o..    | 1 * * ♦ 4 1 0 0 | 6 4 0 0 | 4 6 0 0 | 1 4 0
.o.3.o.3.o.    | * 4 * ♦ 1 0 3 1 | 3 1 3 3 | 3 3 1 3 | 1 3 1
..o3..o3..o    | * * 1 ♦ 0 1 0 4 | 0 4 0 6 | 0 6 0 4 | 0 4 1
---------------+-------+---------+---------+---------+------
oo.3oo.3oo.&#x | 1 1 0 | 4 * * * ♦ 3 1 0 0 | 3 3 0 0 | 1 3 0
o.o3o.o3o.o&#x | 1 0 1 | * 1 * * ♦ 0 4 0 0 | 0 6 0 0 | 0 4 0
.x. ... ...    | 0 2 0 | * * 6 * ♦ 1 0 2 1 | 2 1 1 2 | 1 2 1
.oo3.oo3.oo&#x | 0 1 1 | * * * 4 ♦ 0 1 0 3 | 0 3 0 3 | 0 3 1
---------------+-------+---------+---------+---------+------
ox. ... ...&#x | 1 2 0 | 2 0 1 0 | 6 * * * | 2 1 0 0 | 1 2 0
ooo3ooo3ooo&#x | 1 1 1 | 1 1 0 1 | * 4 * * | 0 3 0 0 | 0 3 0
.x.3.o. ...    | 0 3 0 | 0 0 3 0 | * * 4 * | 1 0 1 1 | 1 1 1
.xo ... ...&#x | 0 2 1 | 0 0 1 2 | * * * 6 | 0 1 0 2 | 0 2 1
---------------+-------+---------+---------+---------+------
ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 | 3 0 1 0 | 4 * * * | 1 1 0
oxo ... ...&#x ♦ 1 2 1 | 2 1 1 2 | 1 2 0 1 | * 6 * * | 0 2 0
.x.3.o.3.o.    ♦ 0 4 0 | 0 0 6 0 | 0 0 4 0 | * * 1 * | 1 0 1
.xo3.oo ...&#x ♦ 0 3 1 | 0 0 3 3 | 0 0 1 3 | * * * 4 | 0 1 1
---------------+-------+---------+---------+---------+------
ox.3oo.3oo.&#x ♦ 1 4 0 | 4 0 6 0 | 6 0 4 0 | 4 0 1 0 | 1 * *
oxo3ooo ...&#x ♦ 1 3 1 | 3 1 3 3 | 3 3 1 3 | 1 3 0 1 | * 4 *
.xo3.oo3.oo&#x ♦ 0 4 1 | 0 0 6 4 | 0 0 4 6 | 0 0 1 4 | * * 1

oxo3ooo oox&#x   → height(1,2) = sqrt(2/3) = 0.816497
                   height(1,3) = sqrt(3)/2 = 0.866025
                   height(2,3) = sqrt(5/12) = 0.645497
( (pt || {3}) || perp line )

o..3o.. o..    | 1 * * ♦ 3 2 0 0 0 | 3 1 6 0 0 0 | 1 6 3 0 0 | 2 3 0
.o.3.o. .o.    | * 3 * ♦ 1 0 2 2 0 | 2 0 2 1 4 1 | 1 4 1 2 2 | 2 2 1
..o3..o ..o    | * * 2 ♦ 0 1 0 3 1 | 0 1 3 0 3 3 | 0 3 3 1 3 | 1 3 1
---------------+-------+-----------+-------------+-----------+------
oo.3oo. oo.&#x | 1 1 0 | 3 * * * * ♦ 2 0 2 0 0 0 | 1 4 1 0 0 | 2 2 0
o.o3o.o o.o&#x | 1 0 1 | * 2 * * * ♦ 0 1 3 0 0 0 | 0 3 3 0 0 | 1 3 0
.x. ... ...    | 0 2 0 | * * 3 * * ♦ 1 0 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.oo3.oo .oo&#x | 0 1 1 | * * * 6 * ♦ 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
... ... ..x    | 0 0 2 | * * * * 1 ♦ 0 1 0 0 0 3 | 0 0 3 0 3 | 0 3 1
---------------+-------+-----------+-------------+-----------+------
ox. ... ...&#x | 1 2 0 | 2 0 1 0 0 | 3 * * * * * | 1 2 0 0 0 | 2 1 0
... ... o.x&#x | 1 0 2 | 0 2 0 0 1 | * 1 * * * * | 0 0 3 0 0 | 0 3 0
ooo3ooo ooo&#x | 1 1 1 | 1 1 0 1 0 | * * 6 * * * | 0 2 1 0 0 | 1 2 0
.x.3.o. ...    | 0 3 0 | 0 0 3 0 0 | * * * 1 * * | 1 0 0 2 0 | 2 0 1
.xo ... ...&#x | 0 2 1 | 0 0 1 2 0 | * * * * 6 * | 0 1 0 1 1 | 1 1 1
... ... .ox&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
---------------+-------+-----------+-------------+-----------+------
ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 0 | 3 0 0 1 0 0 | 1 * * * * | 2 0 0
oxo ... ...&#x ♦ 1 2 1 | 2 1 1 2 0 | 1 0 2 0 1 0 | * 6 * * * | 1 1 0
... ... oox&#x ♦ 1 1 2 | 1 2 0 2 1 | 0 1 2 0 0 1 | * * 3 * * | 0 2 0
.xo3.oo ...&#x ♦ 0 3 1 | 0 0 3 3 0 | 0 0 0 1 3 0 | * * * 2 * | 1 0 1
.xo ... .ox&#x ♦ 0 2 2 | 0 0 1 4 1 | 0 0 0 0 2 2 | * * * * 3 | 0 1 1
---------------+-------+-----------+-------------+-----------+------
oxo3ooo ...&#x ♦ 1 3 1 | 3 1 3 3 0 | 3 0 3 1 3 0 | 1 3 0 1 0 | 2 * *
oxo ... oox&#x ♦ 1 2 2 | 2 2 1 4 1 | 1 1 4 0 2 2 | 0 2 2 0 1 | * 3 *
.xo3.oo .ox&#x ♦ 0 3 2 | 0 0 3 6 1 | 0 0 0 1 6 3 | 0 0 0 2 3 | * * 1

xoo oxo oox&#x   → all heights = 1/sqrt(2) = 0.707107
( (line || perp line) || perp line)

o.. o.. o..    | 2 * * ♦ 1 2 2 0 0 0 | 2 2 1 1 4 0 0 | 4 1 1 2 2 0 | 2 2 1
.o. .o. .o.    | * 2 * ♦ 0 2 0 1 2 0 | 1 0 2 0 4 2 1 | 2 1 0 4 2 1 | 2 1 2
..o ..o ..o    | * * 2 ♦ 0 0 2 0 2 1 | 0 1 0 2 4 1 2 | 2 0 1 2 4 1 | 1 2 2
---------------+-------+-------------+---------------+-------------+------
x.. ... ...    | 2 0 0 | 1 * * * * * ♦ 2 2 0 0 0 0 0 | 4 1 1 0 0 0 | 2 2 0
oo. oo. oo.&#x | 1 1 0 | * 4 * * * * ♦ 1 0 1 0 2 0 0 | 2 1 0 2 1 0 | 2 1 1
o.o o.o o.o&#x | 1 0 1 | * * 4 * * * ♦ 0 1 0 1 2 0 0 | 2 0 1 1 2 0 | 1 2 1
... .x. ...    | 0 2 0 | * * * 1 * * ♦ 0 0 2 0 0 2 0 | 0 1 0 4 0 1 | 2 0 2
.oo .oo .oo&#x | 0 1 1 | * * * * 4 * ♦ 0 0 0 0 2 1 1 | 1 0 0 2 2 1 | 1 1 2
... ... ..x    | 0 0 2 | * * * * * 1 ♦ 0 0 0 2 0 0 2 | 0 0 1 0 4 1 | 0 2 2
---------------+-------+-------------+---------------+-------------+------
xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 2 * * * * * * | 2 1 0 0 0 0 | 2 1 0
x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * 2 * * * * * | 2 0 1 0 0 0 | 1 2 0
... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * 2 * * * * | 0 1 0 2 0 0 | 2 0 1
... ... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * 2 * * * | 0 0 1 0 2 0 | 0 2 1
ooo ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * 8 * * | 1 0 0 1 1 0 | 1 1 1
... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * 2 * | 0 0 0 2 0 1 | 1 0 2
... ... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * 2 | 0 0 0 0 2 1 | 0 1 2
---------------+-------+-------------+---------------+-------------+------
xoo ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 1 1 0 0 2 0 0 | 4 * * * * * | 1 1 0
xo. ox. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 0 2 0 0 0 0 | * 1 * * * * | 2 0 0
x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 2 0 2 0 0 0 | * * 1 * * * | 0 2 0
... oxo ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 0 1 0 2 1 0 | * * * 4 * * | 1 0 1
... ... oox&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 1 2 0 1 | * * * * 4 * | 0 1 1
... .xo .ox&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 2 2 | * * * * * 1 | 0 0 2
---------------+-------+-------------+---------------+-------------+------
xoo oxo ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 2 1 2 0 4 1 0 | 2 1 0 2 0 0 | 2 * *
xoo ... oox&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 1 2 0 2 4 0 1 | 2 0 1 0 2 0 | * 2 *
... oxo oox&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 0 1 1 4 2 2 | 0 0 0 2 2 1 | * * 2

or
o.. o.. o..    & | 6 ♦ 1  4 |  6 4 | 2  8 | 5
-----------------+---+------+------+------+--
x.. ... ...    & | 2 | 3  * ♦  4 0 | 2  4 | 4
oo. oo. oo.&#x & | 2 | * 12 ♦  2 2 | 1  5 | 4
-----------------+---+------+------+------+--
xo. ... ...&#x & | 3 | 1  2 | 12 * | 1  2 | 3
ooo ooo ooo&#x   | 3 | 0  3 |  * 8 | 0  3 | 3
-----------------+---+------+------+------+--
xo. ox. ...&#x & ♦ 4 | 2  4 |  4 0 | 3  * | 2
xoo ... ...&#x & ♦ 4 | 1  5 |  2 2 | * 12 | 2
-----------------+---+------+------+------+--
xoo oxo ...&#x & ♦ 5 | 2  8 |  6 4 | 1  4 | 6

ooox ooxo&#x   → height(1,2) = 1
                 height(1,3) = height(1,4) = height(2,3) = height(2,4) = sqrt(3)/2 = 0.866025
                 height(3,4) = 1/sqrt(2) = 0.707107

o... o...    | 1 * * * ♦ 1 2 2 0 0 0 0 0 | 2 2 1 4 1 0 0 0 0 0 | 1 4 1 2 2 0 0 0 | 2 2 1 0
.o.. .o..    | * 1 * * ♦ 1 0 0 2 2 0 0 0 | 2 2 0 0 0 1 4 1 0 0 | 1 4 1 0 0 2 2 0 | 2 2 0 1
..o. ..o.    | * * 2 * ♦ 0 1 0 1 0 1 2 0 | 1 0 1 2 0 1 2 0 1 2 | 1 2 0 1 2 1 2 1 | 1 2 1 1
...o ...o    | * * * 2 ♦ 0 0 1 0 1 0 2 1 | 0 1 0 2 1 0 2 1 2 1 | 0 2 1 2 1 2 1 1 | 2 1 1 1
-------------+---------+-----------------+---------------------+-----------------+--------
oo.. oo..&#x | 1 1 0 0 | 1 * * * * * * * ♦ 2 2 0 0 0 0 0 0 0 0 | 1 4 1 0 0 0 0 0 | 2 2 0 0
o.o. o.o.&#x | 1 0 1 0 | * 2 * * * * * * ♦ 1 0 1 2 0 0 0 0 0 0 | 1 2 0 1 2 0 0 0 | 1 2 1 0
o..o o..o&#x | 1 0 0 1 | * * 2 * * * * * ♦ 0 1 0 2 1 0 0 0 0 0 | 0 2 1 2 1 0 0 0 | 2 1 1 0
.oo. .oo.&#x | 0 1 1 0 | * * * 2 * * * * ♦ 1 0 0 0 0 1 2 0 0 0 | 1 2 0 0 0 1 2 0 | 1 2 0 1
.o.o .o.o&#x | 0 1 0 1 | * * * * 2 * * * ♦ 0 1 0 0 0 0 2 1 0 0 | 0 2 1 0 0 2 1 0 | 2 1 0 1
.... ..x.    | 0 0 2 0 | * * * * * 1 * * ♦ 0 0 1 0 0 1 0 0 0 2 | 1 0 0 0 2 0 2 1 | 0 2 1 1
..oo ..oo&#x | 0 0 1 1 | * * * * * * 4 * ♦ 0 0 0 1 0 0 1 0 1 1 | 0 1 0 1 1 1 1 1 | 1 1 1 1
...x ....    | 0 0 0 2 | * * * * * * * 1 ♦ 0 0 0 0 1 0 0 1 2 0 | 0 0 1 2 0 2 0 1 | 2 0 1 1
-------------+---------+-----------------+---------------------+-----------------+--------
ooo. ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 0 | 2 * * * * * * * * * | 1 2 0 0 0 0 0 0 | 1 2 0 0
oo.o oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 0 | * 2 * * * * * * * * | 0 2 1 0 0 0 0 0 | 2 1 0 0
.... o.x.&#x | 1 0 2 0 | 0 2 0 0 0 1 0 0 | * * 1 * * * * * * * | 1 0 0 0 2 0 0 0 | 0 2 1 0
o.oo o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 1 0 | * * * 4 * * * * * * | 0 1 0 1 1 0 0 0 | 1 1 1 0
o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 0 1 | * * * * 1 * * * * * | 0 0 1 2 0 0 0 0 | 2 0 1 0
.... .ox.&#x | 0 1 2 0 | 0 0 0 2 0 1 0 0 | * * * * * 1 * * * * | 1 0 0 0 0 0 2 0 | 0 2 0 1
.ooo .ooo&#x | 0 1 1 1 | 0 0 0 1 1 0 1 0 | * * * * * * 4 * * * | 0 1 0 0 0 1 1 0 | 1 1 0 1
.o.x ....&#x | 0 1 0 2 | 0 0 0 0 2 0 0 1 | * * * * * * * 1 * * | 0 0 1 0 0 2 0 0 | 2 0 0 1
..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * 2 * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.... ..xo&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * * 2 | 0 0 0 0 1 0 1 1 | 0 1 1 1
-------------+---------+-----------------+---------------------+-----------------+--------
.... oox.&#x ♦ 1 1 2 0 | 1 2 0 2 0 1 0 0 | 2 0 1 0 0 1 0 0 0 0 | 1 * * * * * * * | 0 2 0 0
oooo oooo&#x ♦ 1 1 1 1 | 1 1 1 1 1 0 1 0 | 1 1 0 1 0 0 1 0 0 0 | * 4 * * * * * * | 1 1 0 0
oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 0 1 | 0 2 0 0 1 0 0 1 0 0 | * * 1 * * * * * | 2 0 0 0
o.ox ....&#x ♦ 1 0 1 2 | 0 1 2 0 0 0 2 1 | 0 0 0 2 1 0 0 0 1 0 | * * * 2 * * * * | 1 0 1 0
.... o.xo&#x ♦ 1 0 2 1 | 0 2 1 0 0 1 2 0 | 0 0 1 2 0 0 0 0 0 1 | * * * * 2 * * * | 0 1 1 0
.oox ....&#x ♦ 0 1 1 2 | 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 2 1 1 0 | * * * * * 2 * * | 1 0 0 1
.... .oxo&#x ♦ 0 1 2 1 | 0 0 0 2 1 1 2 0 | 0 0 0 0 0 1 2 0 0 1 | * * * * * * 2 * | 0 1 0 1
..ox ..xo&#x ♦ 0 0 2 2 | 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 2 2 | * * * * * * * 1 | 0 0 1 1
-------------+---------+-----------------+---------------------+-----------------+--------
ooox ....&#x ♦ 1 1 1 2 | 1 1 2 1 2 0 2 1 | 1 2 0 2 1 0 2 1 1 0 | 0 2 1 1 0 1 0 0 | 2 * * *
.... ooxo&#x ♦ 1 1 2 1 | 1 2 1 2 1 1 2 0 | 2 1 1 2 0 1 2 0 0 1 | 1 2 0 0 1 0 1 0 | * 2 * *
o.ox o.xo&#x ♦ 1 0 2 2 | 0 2 2 0 0 1 4 1 | 0 0 1 4 1 0 0 0 2 2 | 0 0 0 2 2 0 0 1 | * * 1 *
.oox .oxo&#x ♦ 0 1 2 2 | 0 0 0 2 2 1 4 1 | 0 0 0 0 0 1 4 1 2 2 | 0 0 0 0 0 2 2 1 | * * * 1

oooo3ooox&#x   → height(1,2) = height(1,3) = height(2,3) = 1
                height(1,4) = height(2,4) = height(3,4) = sqrt(2/3) = 0.816497

o...3o...    | 1 * * * ♦ 1 1 3 0 0 0 0 | 1 3 3 3 0 0 0 0 | 3 3 3 1 0 0 0 | 3 1 1 0
.o..3.o..    | * 1 * * ♦ 1 0 0 1 3 0 0 | 1 3 0 0 3 3 0 0 | 3 3 0 0 3 1 0 | 3 1 0 1
..o.3..o.    | * * 1 * ♦ 0 1 0 1 0 3 0 | 1 0 3 0 3 0 3 0 | 3 0 3 0 3 0 1 | 3 0 1 1
...o3...o    | * * * 3 ♦ 0 0 1 0 1 1 2 | 0 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1
-------------+---------+---------------+-----------------+---------------+--------
oo..3oo..&#x | 1 1 0 0 | 1 * * * * * * ♦ 1 3 0 0 0 0 0 0 | 3 3 0 0 0 0 0 | 3 1 0 0
o.o.3o.o.&#x | 1 0 1 0 | * 1 * * * * * ♦ 1 0 3 0 0 0 0 0 | 3 0 3 0 0 0 0 | 3 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * 3 * * * * ♦ 0 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
.oo.3.oo.&#x | 0 1 1 0 | * * * 1 * * * ♦ 1 0 0 0 3 0 0 0 | 3 0 0 0 3 0 0 | 3 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * 3 * * ♦ 0 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1
..oo3..oo&#x | 0 0 1 1 | * * * * * 3 * ♦ 0 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1
.... ...x    | 0 0 0 2 | * * * * * * 3 ♦ 0 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
-------------+---------+---------------+-----------------+---------------+--------
ooo.3ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 | 1 * * * * * * * | 3 0 0 0 0 0 0 | 3 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 | * 3 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
o.oo3o.oo&#x | 1 0 1 1 | 0 1 1 0 0 1 0 | * * 3 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
.... o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 1 | * * * 3 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 | * * * * 3 * * * | 1 0 0 0 2 0 0 | 2 0 0 1
.... .o.x&#x | 0 1 0 2 | 0 0 0 0 2 0 1 | * * * * * 3 * * | 0 1 0 0 1 1 0 | 1 1 0 1
.... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * 3 * | 0 0 1 0 1 0 1 | 1 0 1 1
...o3...x&#x | 0 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * 1 | 0 0 0 1 0 1 1 | 0 1 1 1
-------------+---------+---------------+-----------------+---------------+--------
oooo3oooo&#x ♦ 1 1 1 1 | 1 1 1 1 1 1 0 | 1 1 1 0 1 0 0 0 | 3 * * * * * * | 2 0 0 0
.... oo.x&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 1 | 0 2 0 1 0 1 0 0 | * 3 * * * * * | 1 1 0 0
.... o.ox&#x ♦ 1 0 1 2 | 0 1 2 0 0 2 1 | 0 0 2 1 0 0 1 0 | * * 3 * * * * | 1 0 1 0
o..o3o..x&#x ♦ 1 0 0 3 | 0 0 3 0 0 0 3 | 0 0 0 3 0 0 0 1 | * * * 1 * * * | 0 1 1 0
.... .oox&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 1 | 0 0 0 0 2 1 1 0 | * * * * 3 * * | 1 0 0 1
.o.o3.o.x&#x ♦ 0 1 0 3 | 0 0 0 0 3 0 3 | 0 0 0 0 0 3 0 1 | * * * * * 1 * | 0 1 0 1
..oo3..ox&#x ♦ 0 0 1 3 | 0 0 0 0 0 3 3 | 0 0 0 0 0 0 3 1 | * * * * * * 1 | 0 0 1 1
-------------+---------+---------------+-----------------+---------------+--------
.... ooox&#x ♦ 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 0 | 2 1 1 0 1 0 0 | 3 * * *
oo.o3oo.x&#x ♦ 1 1 0 3 | 1 0 3 0 3 0 3 | 0 3 0 3 0 3 0 1 | 0 3 0 1 0 1 0 | * 1 * *
o.oo3o.ox&#x ♦ 1 0 1 3 | 0 1 3 0 0 3 3 | 0 0 3 3 0 0 3 1 | 0 0 3 1 0 0 1 | * * 1 *
.ooo3.oox&#x ♦ 0 1 1 3 | 0 0 0 1 3 3 3 | 0 0 0 0 3 3 3 1 | 0 0 0 0 3 1 1 | * * * 1

oooox&#x   → height(1,2) = height(1,3) = height(1,4) = height(2,3) = height(2,4) = height(3,4) = 1
             height(1,5) = height(2,5) = height(3,5) = height(4,5) = sqrt(3)/2 = 0.866025

o....    | 1 * * * * ♦ 1 1 1 2 0 0 0 0 0 0 0 | 1 1 2 1 2 2 1 0 0 0 0 0 0 0 | 1 2 2 1 2 1 1 0 0 0 0 | 2 1 1 1 0
.o...    | * 1 * * * ♦ 1 0 0 0 1 1 2 0 0 0 0 | 1 1 2 0 0 0 0 1 2 2 1 0 0 0 | 1 2 2 1 0 0 0 2 1 1 0 | 2 1 1 0 1
..o..    | * * 1 * * ♦ 0 1 0 0 1 0 0 1 2 0 0 | 1 0 0 1 2 0 0 1 2 0 0 2 1 0 | 1 2 0 0 2 1 0 2 1 0 1 | 2 1 0 1 1
...o.    | * * * 1 * ♦ 0 0 1 0 0 1 0 1 0 2 0 | 0 1 0 1 0 2 0 1 0 2 0 2 0 1 | 1 0 2 0 2 0 1 2 0 1 1 | 2 0 1 1 1
....o    | * * * * 2 ♦ 0 0 0 1 0 0 1 0 1 1 1 | 0 0 1 0 1 1 1 0 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------+-----------+-----------------------+-----------------------------+-----------------------+----------
oo...&#x | 1 1 0 0 0 | 1 * * * * * * * * * * ♦ 1 1 2 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 0 0 | 2 1 1 0 0
o.o..&#x | 1 0 1 0 0 | * 1 * * * * * * * * * ♦ 1 0 0 1 2 0 0 0 0 0 0 0 0 0 | 1 2 0 0 2 1 0 0 0 0 0 | 2 1 0 1 0
o..o.&#x | 1 0 0 1 0 | * * 1 * * * * * * * * ♦ 0 1 0 1 0 2 0 0 0 0 0 0 0 0 | 1 0 2 0 2 0 1 0 0 0 0 | 2 0 1 1 0
o...o&#x | 1 0 0 0 1 | * * * 2 * * * * * * * ♦ 0 0 1 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.oo..&#x | 0 1 1 0 0 | * * * * 1 * * * * * * ♦ 1 0 0 0 0 0 0 1 2 0 0 0 0 0 | 1 2 0 0 0 0 0 2 1 0 0 | 2 1 0 0 1
.o.o.&#x | 0 1 0 1 0 | * * * * * 1 * * * * * ♦ 0 1 0 0 0 0 0 1 0 2 0 0 0 0 | 1 0 2 0 0 0 0 2 0 1 0 | 2 0 1 0 1
.o..o&#x | 0 1 0 0 1 | * * * * * * 2 * * * * ♦ 0 0 1 0 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
..oo.&#x | 0 0 1 1 0 | * * * * * * * 1 * * * ♦ 0 0 0 1 0 0 0 1 0 0 0 2 0 0 | 1 0 0 0 2 0 0 2 0 0 1 | 2 0 0 1 1
..o.o&#x | 0 0 1 0 1 | * * * * * * * * 2 * * ♦ 0 0 0 0 1 0 0 0 1 0 0 1 1 0 | 0 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
...oo&#x | 0 0 0 1 1 | * * * * * * * * * 2 * ♦ 0 0 0 0 0 1 0 0 0 1 0 1 0 1 | 0 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1
....x    | 0 0 0 0 2 | * * * * * * * * * * 1 ♦ 0 0 0 0 0 0 1 0 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------+-----------+-----------------------+-----------------------------+-----------------------+----------
ooo..&#x | 1 1 1 0 0 | 1 1 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0
oo.o.&#x | 1 1 0 1 0 | 1 0 1 0 0 1 0 0 0 0 0 | * 1 * * * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 | 2 0 1 0 0
oo..o&#x | 1 1 0 0 1 | 1 0 0 1 0 0 1 0 0 0 0 | * * 2 * * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
o.oo.&#x | 1 0 1 1 0 | 0 1 1 0 0 0 0 1 0 0 0 | * * * 1 * * * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 | 2 0 0 1 0
o.o.o&#x | 1 0 1 0 1 | 0 1 0 1 0 0 0 0 1 0 0 | * * * * 2 * * * * * * * * * | 0 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
o..oo&#x | 1 0 0 1 1 | 0 0 1 1 0 0 0 0 0 1 0 | * * * * * 2 * * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
o...x&#x | 1 0 0 0 2 | 0 0 0 2 0 0 0 0 0 0 1 | * * * * * * 1 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.ooo.&#x | 0 1 1 1 0 | 0 0 0 0 1 1 0 1 0 0 0 | * * * * * * * 1 * * * * * * | 1 0 0 0 0 0 0 2 0 0 0 | 2 0 0 0 1
.oo.o&#x | 0 1 1 0 1 | 0 0 0 0 1 0 1 0 1 0 0 | * * * * * * * * 2 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.o.oo&#x | 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * * 2 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.o..x&#x | 0 1 0 0 2 | 0 0 0 0 0 0 2 0 0 0 1 | * * * * * * * * * * 1 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
..ooo&#x | 0 0 1 1 1 | 0 0 0 0 0 0 0 1 1 1 0 | * * * * * * * * * * * 2 * * | 0 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
..o.x&#x | 0 0 1 0 2 | 0 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * 1 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
...ox&#x | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------+-----------+-----------------------+-----------------------------+-----------------------+----------
oooo.&#x ♦ 1 1 1 1 0 | 1 1 1 0 1 1 0 1 0 0 0 | 1 1 0 1 0 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * | 2 0 0 0 0
ooo.o&#x ♦ 1 1 1 0 1 | 1 1 0 1 1 0 1 0 1 0 0 | 1 0 1 0 1 0 0 0 1 0 0 0 0 0 | * 2 * * * * * * * * * | 1 1 0 0 0
oo.oo&#x ♦ 1 1 0 1 1 | 1 0 1 1 0 1 1 0 0 1 0 | 0 1 1 0 0 1 0 0 0 1 0 0 0 0 | * * 2 * * * * * * * * | 1 0 1 0 0
oo..x&#x ♦ 1 1 0 0 2 | 1 0 0 2 0 0 2 0 0 0 1 | 0 0 2 0 0 0 1 0 0 0 1 0 0 0 | * * * 1 * * * * * * * | 0 1 1 0 0 
o.ooo&#x ♦ 1 0 1 1 1 | 0 1 1 1 0 0 0 1 1 1 0 | 0 0 0 1 1 1 0 0 0 0 0 1 0 0 | * * * * 2 * * * * * * | 1 0 0 1 0
o.o.x&#x ♦ 1 0 1 0 2 | 0 1 0 2 0 0 0 0 2 0 1 | 0 0 0 0 2 0 1 0 0 0 0 0 1 0 | * * * * * 1 * * * * * | 0 1 0 1 0
o..ox&#x ♦ 1 0 0 1 2 | 0 0 1 2 0 0 0 0 0 2 1 | 0 0 0 0 0 2 1 0 0 0 0 0 0 1 | * * * * * * 1 * * * * | 0 0 1 1 0
.oooo&#x ♦ 0 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 0 | 0 0 0 0 0 0 0 1 1 1 0 1 0 0 | * * * * * * * 2 * * * | 1 0 0 0 1
.oo.x&#x ♦ 0 1 1 0 2 | 0 0 0 0 1 0 2 0 2 0 1 | 0 0 0 0 0 0 0 0 2 0 1 0 1 0 | * * * * * * * * 1 * * | 0 1 0 0 1
.o.ox&#x ♦ 0 1 0 1 2 | 0 0 0 0 0 1 2 0 0 2 1 | 0 0 0 0 0 0 0 0 0 2 1 0 0 1 | * * * * * * * * * 1 * | 0 0 1 0 1
..oox&#x ♦ 0 0 1 1 2 | 0 0 0 0 0 0 0 1 2 2 1 | 0 0 0 0 0 0 0 0 0 0 0 2 1 1 | * * * * * * * * * * 1 | 0 0 0 1 1
---------+-----------+-----------------------+-----------------------------+-----------------------+----------
ooooo&#x ♦ 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 0 | 1 1 1 1 1 1 0 1 1 1 0 1 0 0 | 1 1 1 0 1 0 0 1 0 0 0 | 2 * * * *
ooo.x&#x ♦ 1 1 1 0 2 | 1 1 0 2 1 0 2 0 2 0 1 | 1 0 2 0 2 0 1 0 2 0 1 0 1 0 | 0 2 0 1 0 1 0 0 1 0 0 | * 1 * * *
oo.ox&#x ♦ 1 1 0 1 2 | 1 0 1 2 0 1 2 0 0 2 1 | 0 1 2 0 0 2 1 0 0 2 1 0 0 1 | 0 0 2 1 0 0 1 0 0 1 0 | * * 1 * *
o.oox&#x ♦ 1 0 1 1 2 | 0 1 1 2 0 0 0 1 2 2 1 | 0 0 0 1 2 2 1 0 0 0 0 2 1 1 | 0 0 0 0 2 1 1 0 0 0 1 | * * * 1 *
.ooox&#x ♦ 0 1 1 1 2 | 0 0 0 0 1 1 2 1 2 2 1 | 0 0 0 0 0 0 0 1 2 2 1 2 1 1 | 0 0 0 0 0 0 0 2 1 1 1 | * * * * 1

oooooo&#x   → all pairwise heights = 1

o.....    | 1 * * * * * ♦ 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 0
.o....    | * 1 * * * * ♦ 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 | 1 1 1 1 0 1
..o...    | * * 1 * * * ♦ 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 | 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 | 1 1 1 0 1 1
...o..    | * * * 1 * * ♦ 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 | 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 | 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 | 1 1 0 1 1 1
....o.    | * * * * 1 * ♦ 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 | 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 | 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 | 1 0 1 1 1 1
.....o    | * * * * * 1 ♦ 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 | 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 | 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
----------+-------------+-------------------------------+-----------------------------------------+-------------------------------+------------
oo....&#x | 1 1 0 0 0 0 | 1 * * * * * * * * * * * * * * ♦ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
o.o...&#x | 1 0 1 0 0 0 | * 1 * * * * * * * * * * * * * ♦ 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 1 0
o..o..&#x | 1 0 0 1 0 0 | * * 1 * * * * * * * * * * * * ♦ 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0
o...o.&#x | 1 0 0 0 1 0 | * * * 1 * * * * * * * * * * * ♦ 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 | 1 0 1 1 1 0
o....o&#x | 1 0 0 0 0 1 | * * * * 1 * * * * * * * * * * ♦ 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.oo...&#x | 0 1 1 0 0 0 | * * * * * 1 * * * * * * * * * ♦ 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
.o.o..&#x | 0 1 0 1 0 0 | * * * * * * 1 * * * * * * * * ♦ 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
.o..o.&#x | 0 1 0 0 1 0 | * * * * * * * 1 * * * * * * * ♦ 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.o...o&#x | 0 1 0 0 0 1 | * * * * * * * * 1 * * * * * * ♦ 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..oo..&#x | 0 0 1 1 0 0 | * * * * * * * * * 1 * * * * * ♦ 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 | 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1
..o.o.&#x | 0 0 1 0 1 0 | * * * * * * * * * * 1 * * * * ♦ 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 | 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1
..o..o&#x | 0 0 1 0 0 1 | * * * * * * * * * * * 1 * * * ♦ 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
...oo.&#x | 0 0 0 1 1 0 | * * * * * * * * * * * * 1 * * ♦ 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 | 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 | 1 0 0 1 1 1
...o.o&#x | 0 0 0 1 0 1 | * * * * * * * * * * * * * 1 * ♦ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 | 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
....oo&#x | 0 0 0 0 1 1 | * * * * * * * * * * * * * * 1 ♦ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 | 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
----------+-------------+-------------------------------+-----------------------------------------+-------------------------------+------------
ooo...&#x | 1 1 1 0 0 0 | 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo.o..&#x | 1 1 0 1 0 0 | 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 | * 1 * * * * * * * * * * * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
oo..o.&#x | 1 1 0 0 1 0 | 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 | * * 1 * * * * * * * * * * * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
oo...o&#x | 1 1 0 0 0 1 | 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 | * * * 1 * * * * * * * * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.oo..&#x | 1 0 1 1 0 0 | 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 | * * * * 1 * * * * * * * * * * * * * * * | 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
o.o.o.&#x | 1 0 1 0 1 0 | 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 | * * * * * 1 * * * * * * * * * * * * * * | 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
o.o..o&#x | 1 0 1 0 0 1 | 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 | * * * * * * 1 * * * * * * * * * * * * * | 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
o..oo.&#x | 1 0 0 1 1 0 | 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * * 1 * * * * * * * * * * * * | 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
o..o.o&#x | 1 0 0 1 0 1 | 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * 1 * * * * * * * * * * * | 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
o...oo&#x | 1 0 0 0 1 1 | 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 1 * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.ooo..&#x | 0 1 1 1 0 0 | 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | * * * * * * * * * * 1 * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.oo.o.&#x | 0 1 1 0 1 0 | 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 | * * * * * * * * * * * 1 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
.oo..o&#x | 0 1 1 0 0 1 | 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 | * * * * * * * * * * * * 1 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.o.oo.&#x | 0 1 0 1 1 0 | 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 | * * * * * * * * * * * * * 1 * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
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.o..oo&#x | 0 1 0 0 1 1 | 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 | * * * * * * * * * * * * * * * 1 * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..ooo.&#x | 0 0 1 1 1 0 | 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 | * * * * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1
..oo.o&#x | 0 0 1 1 0 1 | 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 | * * * * * * * * * * * * * * * * * 1 * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..o.oo&#x | 0 0 1 0 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 | * * * * * * * * * * * * * * * * * * 1 * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
...ooo&#x | 0 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
----------+-------------+-------------------------------+-----------------------------------------+-------------------------------+------------
oooo..&#x ♦ 1 1 1 1 0 0 | 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 1 0 0 0 0
ooo.o.&#x ♦ 1 1 1 0 1 0 | 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 | 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | * 1 * * * * * * * * * * * * * | 1 0 1 0 0 0
ooo..o&#x ♦ 1 1 1 0 0 1 | 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 | 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 | * * 1 * * * * * * * * * * * * | 0 1 1 0 0 0
oo.oo.&#x ♦ 1 1 0 1 1 0 | 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 | 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 | * * * 1 * * * * * * * * * * * | 1 0 0 1 0 0
oo.o.o&#x ♦ 1 1 0 1 0 1 | 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 | 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * 1 * * * * * * * * * * | 0 1 0 1 0 0
oo..oo&#x ♦ 1 1 0 0 1 1 | 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 | 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 | * * * * * 1 * * * * * * * * * | 0 0 1 1 0 0
o.ooo.&#x ♦ 1 0 1 1 1 0 | 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 | 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.oo.o&#x ♦ 1 0 1 1 0 1 | 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * * 1 * * * * * * * | 0 1 0 0 1 0
o.o.oo&#x ♦ 1 0 1 0 1 1 | 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 | 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * 1 * * * * * * | 0 0 1 0 1 0
o..ooo&#x ♦ 1 0 0 1 1 1 | 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.oooo.&#x ♦ 0 1 1 1 1 0 | 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.ooo.o&#x ♦ 0 1 1 1 0 1 | 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 | 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 | * * * * * * * * * * * 1 * * * | 0 1 0 0 0 1
.oo.oo&#x ♦ 0 1 1 0 1 1 | 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 | * * * * * * * * * * * * 1 * * | 0 0 1 0 0 1
.o.ooo&#x ♦ 0 1 0 1 1 1 | 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 | * * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..oooo&#x ♦ 0 0 1 1 1 1 | 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 | * * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
----------+-------------+-------------------------------+-----------------------------------------+-------------------------------+------------
ooooo.&#x ♦ 1 1 1 1 1 0 | 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 | 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 | 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
oooo.o&#x ♦ 1 1 1 1 0 1 | 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 | 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 | 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 | * 1 * * * *
ooo.oo&#x ♦ 1 1 1 0 1 1 | 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 | 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 | 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 | * * 1 * * *
oo.ooo&#x ♦ 1 1 0 1 1 1 | 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 | 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 | 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.oooo&#x ♦ 1 0 1 1 1 1 | 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 | 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 | * * * * 1 *
.ooooo&#x ♦ 0 1 1 1 1 1 | 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 | * * * * * 1

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