﻿ trahip
 Acronym trahip (old: thiddippip) Name triangle hexagonal-prism duoprism,triangle-hexagon duoprismatic prism Circumradius sqrt(19/12) = 1.258306 Volume 9/8 = 1.125 Confer more general: n,m-dippip   general polytopal classes: segmentotera   lace simplices Externallinks

Incidence matrix according to Dynkin symbol

```x x3o x6o

. . . . . | 36 |  1  2  2 |  2  2  1  4 1 | 1  4 1  2 2 | 2 2 1
----------+----+----------+---------------+-------------+------
x . . . . |  2 | 18  *  * |  2  2  0  0 0 | 1  4 1  0 0 | 2 2 0
. x . . . |  2 |  * 36  * |  1  0  1  2 0 | 1  2 0  2 1 | 2 1 1
. . . x . |  2 |  *  * 36 |  0  1  0  2 1 | 0  2 1  1 2 | 1 2 1
----------+----+----------+---------------+-------------+------
x x . . . |  4 |  2  2  0 | 18  *  *  * * | 1  2 0  0 0 | 2 1 0
x . . x . |  4 |  2  0  2 |  * 18  *  * * | 0  2 1  0 0 | 1 2 0
. x3o . . |  3 |  0  3  0 |  *  * 12  * * | 1  0 0  2 0 | 2 0 1
. x . x . |  4 |  0  2  2 |  *  *  * 36 * | 0  1 0  1 1 | 1 1 1
. . . x6o |  6 |  0  0  6 |  *  *  *  * 6 | 0  0 1  0 2 | 0 2 1
----------+----+----------+---------------+-------------+------
x x3o . . ♦  6 |  3  6  0 |  3  0  2  0 0 | 6  * *  * * | 2 0 0
x x . x . ♦  8 |  4  4  4 |  2  2  0  2 0 | * 18 *  * * | 1 1 0
x . . x6o ♦ 12 |  6  0 12 |  0  6  0  0 2 | *  * 3  * * | 0 2 0
. x3o x . ♦  6 |  0  6  3 |  0  0  2  3 0 | *  * * 12 * | 1 0 1
. x . x6o ♦ 12 |  0  6 12 |  0  0  0  6 2 | *  * *  * 6 | 0 1 1
----------+----+----------+---------------+-------------+------
x x3o x . ♦ 12 |  6 12  6 |  6  3  4  6 0 | 2  3 0  2 0 | 6 * *
x x . x6o ♦ 24 | 12 12 24 |  6 12  0 12 4 | 0  6 2  0 2 | * 3 *
. x3o x6o ♦ 18 |  0 18 18 |  0  0  6 18 3 | 0  0 0  6 3 | * * 2
```

```x o3x x3x

o o3o o3o | 36 |  1  2  1  1 |  2 1 1  1  2  2 1 | 1 2 2 1 1 1 2 | 1 1 2 1
----------+----+-------------+-------------------+---------------+--------
x . . . . |  2 | 18  *  *  * |  2 1 1  0  0  0 0 | 1 2 2 1 0 0 0 | 1 1 2 0
. . x . . |  2 |  * 36  *  * |  1 0 0  1  1  1 0 | 1 1 1 0 1 1 1 | 1 1 1 1
. . . x . |  2 |  *  * 18  * |  0 1 0  0  2  0 1 | 0 2 0 1 1 0 2 | 1 0 2 1
. . . . x |  2 |  *  *  * 18 |  0 0 1  0  0  2 1 | 0 0 2 1 0 1 2 | 0 1 2 1
----------+----+-------------+-------------------+---------------+--------
x . x . . |  4 |  2  2  0  0 | 18 * *  *  *  * * | 1 1 1 0 0 0 0 | 1 1 1 0
x . . x . |  4 |  2  0  2  0 |  * 9 *  *  *  * * | 0 2 0 1 0 0 0 | 1 0 2 0
x . . . x |  4 |  2  0  0  2 |  * * 9  *  *  * * | 0 0 2 1 0 0 0 | 0 1 2 0
. o3x . . |  3 |  0  3  0  0 |  * * * 12  *  * * | 1 0 0 0 1 1 0 | 1 1 0 1
. . x x . |  4 |  0  2  2  0 |  * * *  * 18  * * | 0 1 0 0 1 0 1 | 1 0 1 1
. . x . x |  4 |  0  2  0  2 |  * * *  *  * 18 * | 0 0 1 0 0 1 1 | 0 1 1 1
. . . x3x |  6 |  0  0  3  3 |  * * *  *  *  * 6 | 0 0 0 1 0 0 2 | 0 0 2 1
----------+----+-------------+-------------------+---------------+--------
x o3x . . ♦  6 |  3  6  0  0 |  3 0 0  2  0  0 0 | 6 * * * * * * | 1 1 0 0
x . x x . ♦  8 |  4  4  4  0 |  2 2 0  0  2  0 0 | * 9 * * * * * | 1 0 1 0
x . x . x ♦  8 |  4  4  0  4 |  2 0 2  0  0  2 0 | * * 9 * * * * | 0 1 1 0
x . . x3x ♦ 12 |  6  0  6  6 |  0 3 3  0  0  0 2 | * * * 3 * * * | 0 0 2 0
. o3x x . ♦  6 |  0  6  3  0 |  0 0 0  2  3  0 0 | * * * * 6 * * | 1 0 0 1
. o3x . x ♦  6 |  0  6  0  3 |  0 0 0  2  0  3 0 | * * * * * 6 * | 0 1 0 1
. . x x3x ♦ 12 |  0  6  6  6 |  0 0 0  0  3  3 2 | * * * * * * 6 | 0 0 1 1
----------+----+-------------+-------------------+---------------+--------
x o3x x . ♦ 12 |  6 12  6  0 |  6 3 0  4  6  0 0 | 2 3 0 0 2 0 0 | 3 * * *
x o3x . x ♦ 12 |  6 12  0  6 |  6 0 3  4  0  6 0 | 2 0 3 0 0 2 0 | * 3 * *
x . x x3x ♦ 24 | 12 12 12 12 |  6 6 6  0  6  6 4 | 0 3 3 2 0 0 2 | * * 3 *
. o3x x3x ♦ 18 |  0 18  9  9 |  0 0 0  6  9  9 3 | 0 0 0 0 3 3 3 | * * * 2
```

```xx3oo xx6oo&#x   → height = 1
(thiddip || thiddip)

o.3o. o.6o.    | 18  * |  2  2  1  0  0 | 1  4 1  2  2 0  0 0 | 2 2 1  4 1 0 0 | 1 2 2 0
.o3.o .o6.o    |  * 18 |  0  0  1  2  2 | 0  0 0  2  2 1  4 1 | 0 0 1  4 1 2 2 | 0 2 2 1
---------------+-------+----------------+---------------------+----------------+--------
x. .. .. ..    |  2  0 | 18  *  *  *  * | 1  2 0  1  0 0  0 0 | 2 1 1  2 0 0 0 | 1 2 1 0
.. .. x. ..    |  2  0 |  * 18  *  *  * | 0  2 1  0  1 0  0 0 | 1 2 0  2 1 0 0 | 1 1 2 0
oo3oo oo6oo&#x |  1  1 |  *  * 18  *  * | 0  0 0  2  2 0  0 0 | 0 0 1  4 1 0 0 | 0 2 2 0
.x .. .. ..    |  0  2 |  *  *  * 18  * | 0  0 0  1  0 1  2 0 | 0 0 1  2 0 2 1 | 0 2 1 1
.. .. .x ..    |  0  2 |  *  *  *  * 18 | 0  0 0  0  1 0  2 1 | 0 0 0  2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. .. ..    |  3  0 |  3  0  0  0  0 | 6  * *  *  * *  * * | 2 0 1  0 0 0 0 | 1 2 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 18 *  *  * *  * * | 1 1 0  1 0 0 0 | 1 1 1 0
.. .. x.6o.    |  6  0 |  0  6  0  0  0 | *  * 3  *  * *  * * | 0 2 0  0 1 0 0 | 1 0 2 0
xx .. .. ..&#x |  2  2 |  1  0  2  1  0 | *  * * 18  * *  * * | 0 0 1  2 0 0 0 | 0 2 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  * 18 *  * * | 0 0 0  2 1 0 0 | 0 1 2 0
.x3.o .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  * 6  * * | 0 0 1  0 0 2 0 | 0 2 0 1
.x .. .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  * * 18 * | 0 0 0  1 0 1 1 | 0 1 1 1
.. .. .x6.o    |  0  6 |  0  0  0  0  6 | *  * *  *  * *  * 3 | 0 0 0  0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x. ..    ♦  6  0 |  6  3  0  0  0 | 2  3 0  0  0 0  0 0 | 6 * *  * * * * | 1 1 0 0
x. .. x.6o.    ♦ 12  0 |  6 12  0  0  0 | 0  6 2  0  0 0  0 0 | * 3 *  * * * * | 1 0 1 0
xx3oo .. ..&#x ♦  3  3 |  3  0  3  3  0 | 1  0 0  3  0 1  0 0 | * * 6  * * * * | 0 2 0 0
xx .. xx ..&#x ♦  4  4 |  2  2  4  2  2 | 0  1 0  2  2 0  1 0 | * * * 18 * * * | 0 1 1 0
.. .. xx6oo&#x ♦  6  6 |  0  6  6  0  6 | 0  0 1  0  6 0  0 1 | * * *  * 3 * * | 0 0 2 0
.x3.o .x ..    ♦  0  6 |  0  0  0  6  3 | 0  0 0  0  0 2  3 0 | * * *  * * 6 * | 0 1 0 1
.x .. .x6.o    ♦  0 12 |  0  0  0  6 12 | 0  0 0  0  0 0  6 2 | * * *  * * * 3 | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x.6o.    ♦ 18  0 | 18 18  0  0  0 | 6 18 3  0  0 0  0 0 | 6 3 0  0 0 0 0 | 1 * * *
xx3oo xx ..&#x ♦  6  6 |  6  3  6  6  3 | 2  3 0  6  3 2  3 0 | 1 0 2  3 0 1 0 | * 6 * *
xx .. xx6oo&#x ♦ 12 12 |  6 12 12  6 12 | 0  6 2  6 12 0  6 2 | 0 1 0  6 2 0 1 | * * 3 *
.x3.o .x6.o    ♦  0 18 |  0  0  0 18 18 | 0  0 0  0  0 6 18 3 | 0 0 0  0 0 6 3 | * * * 1
```

```xx3oo xx3xx&#x   → height = 1
(thiddip || thiddip)

o.3o. o.3o.    | 18  * |  2 1 1  1  0 0 0 | 1 2 2 1  2 1 1 0 0 0 0 | 1 1 2 1 2 2 1 0 0 0 | 1 1 1 2 0
.o3.o .o3.o    |  * 18 |  0 0 0  1  2 1 1 | 0 0 0 0  2 1 1 1 2 2 1 | 0 0 0 1 2 2 1 1 1 2 | 0 1 1 2 1
---------------+-------+------------------+------------------------+---------------------+----------
x. .. .. ..    |  2  0 | 18 * *  *  * * * | 1 1 1 0  1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.. .. x. ..    |  2  0 |  * 9 *  *  * * * | 0 2 0 1  0 1 0 0 0 0 0 | 1 0 2 0 2 0 1 0 0 0 | 1 1 0 2 0
.. .. .. x.    |  2  0 |  * * 9  *  * * * | 0 0 2 1  0 0 1 0 0 0 0 | 0 1 2 0 0 2 1 0 0 0 | 1 0 1 2 0
oo3oo oo3oo&#x |  1  1 |  * * * 18  * * * | 0 0 0 0  2 1 1 0 0 0 0 | 0 0 0 1 2 2 1 0 0 0 | 0 1 1 2 0
.x .. .. ..    |  0  2 |  * * *  * 18 * * | 0 0 0 0  1 0 0 1 1 1 0 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
.. .. .x ..    |  0  2 |  * * *  *  * 9 * | 0 0 0 0  0 1 0 0 2 0 1 | 0 0 0 0 2 0 1 1 0 2 | 0 1 0 2 1
.. .. .. .x    |  0  2 |  * * *  *  * * 9 | 0 0 0 0  0 0 1 0 0 2 1 | 0 0 0 0 0 2 1 0 1 2 | 0 0 1 2 1
---------------+-------+------------------+------------------------+---------------------+----------
x.3o. .. ..    |  3  0 |  3 0 0  0  0 0 0 | 6 * * *  * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
x. .. x. ..    |  4  0 |  2 2 0  0  0 0 0 | * 9 * *  * * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
x. .. .. x.    |  4  0 |  2 0 2  0  0 0 0 | * * 9 *  * * * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
.. .. x.3x.    |  6  0 |  0 3 3  0  0 0 0 | * * * 3  * * * * * * * | 0 0 2 0 0 0 1 0 0 0 | 1 0 0 2 0
xx .. .. ..&#x |  2  2 |  1 0 0  2  1 0 0 | * * * * 18 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.. .. xx ..&#x |  2  2 |  0 1 0  2  0 1 0 | * * * *  * 9 * * * * * | 0 0 0 0 2 0 1 0 0 0 | 0 1 0 2 0
.. .. .. xx&#x |  2  2 |  0 0 1  2  0 0 1 | * * * *  * * 9 * * * * | 0 0 0 0 0 2 1 0 0 0 | 0 0 1 2 0
.x3.o .. ..    |  0  3 |  0 0 0  0  3 0 0 | * * * *  * * * 6 * * * | 0 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1
.x .. .x ..    |  0  4 |  0 0 0  0  2 2 0 | * * * *  * * * * 9 * * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.x .. .. .x    |  0  4 |  0 0 0  0  2 0 2 | * * * *  * * * * * 9 * | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
.. .. .x3.x    |  0  6 |  0 0 0  0  0 3 3 | * * * *  * * * * * * 3 | 0 0 0 0 0 0 1 0 0 2 | 0 0 0 2 1
---------------+-------+------------------+------------------------+---------------------+----------
x.3o. x. ..    ♦  6  0 |  6 3 0  0  0 0 0 | 2 3 0 0  0 0 0 0 0 0 0 | 3 * * * * * * * * * | 1 1 0 0 0
x.3o. .. x.    ♦  6  0 |  6 0 3  0  0 0 0 | 2 0 3 0  0 0 0 0 0 0 0 | * 3 * * * * * * * * | 1 0 1 0 0
x. .. x.3x.    ♦ 12  0 |  6 6 6  0  0 0 0 | 0 3 3 2  0 0 0 0 0 0 0 | * * 3 * * * * * * * | 1 0 0 1 0
xx3oo .. ..&#x ♦  3  3 |  3 0 0  3  3 0 0 | 1 0 0 0  3 0 0 1 0 0 0 | * * * 6 * * * * * * | 0 1 1 0 0
xx .. xx ..&#x ♦  4  4 |  2 2 0  4  2 2 0 | 0 1 0 0  2 2 0 0 1 0 0 | * * * * 9 * * * * * | 0 1 0 1 0
xx .. .. xx&#x ♦  4  4 |  2 0 2  4  2 0 2 | 0 0 1 0  2 0 2 0 0 1 0 | * * * * * 9 * * * * | 0 0 1 1 0
.. .. xx3xx&#x ♦  6  6 |  0 3 3  6  0 3 3 | 0 0 0 1  0 3 3 0 0 0 1 | * * * * * * 3 * * * | 0 0 0 2 0
.x3.o .x ..    ♦  0  6 |  0 0 0  0  6 3 0 | 0 0 0 0  0 0 0 2 3 0 0 | * * * * * * * 3 * * | 0 1 0 0 1
.x3.o .. .x    ♦  0  6 |  0 0 0  0  6 0 3 | 0 0 0 0  0 0 0 2 0 3 0 | * * * * * * * * 3 * | 0 0 1 0 1
.x .. .x3.x    ♦  0 12 |  0 0 0  0  6 6 6 | 0 0 0 0  0 0 0 0 3 3 2 | * * * * * * * * * 3 | 0 0 0 1 1
---------------+-------+------------------+------------------------+---------------------+----------
x.3o. x.3x.    ♦ 18  0 | 18 9 9  0  0 0 0 | 6 9 9 3  0 0 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 0 | 1 * * * *
xx3oo xx ..&#x ♦  6  6 |  6 3 0  6  6 3 0 | 2 3 0 0  6 3 0 2 3 0 0 | 1 0 0 2 3 0 0 1 0 0 | * 3 * * *
xx3oo .. xx&#x ♦  6  6 |  6 0 3  6  6 0 3 | 2 0 3 0  6 0 3 2 0 3 0 | 0 1 0 2 0 3 0 0 1 0 | * * 3 * *
xx .. xx3xx&#x ♦ 12 12 |  6 6 6 12  6 6 6 | 0 3 3 2  6 6 6 0 3 3 2 | 0 0 1 0 3 3 2 0 0 1 | * * * 3 *
.x3.o .x3.x    ♦  0 18 |  0 0 0  0 18 9 9 | 0 0 0 0  0 0 0 6 9 9 3 | 0 0 0 0 0 0 0 3 3 3 | * * * * 1
```

```ox xx xx6oo&#x   → height = sqrt(3)/2 = 0.866025
(hip || shiddip)

o. o. o.6o.    | 12  * | 1  2  2  0  0  0 | 2 1  1  2  4 0  0  0 0 | 1 1  2  4 2 0 0 0 | 2 1 2 0
.o .o .o6.o    |  * 24 | 0  0  1  1  1  2 | 0 0  1  1  2 1  2  2 1 | 0 1  2  2 1 2 1 1 | 2 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. .. ..    |  2  0 | 6  *  *  *  *  * | 2 0  0  2  0 0  0  0 0 | 1 1  0  4 0 0 0 0 | 2 0 2 0
.. .. x. ..    |  2  0 | * 12  *  *  *  * | 1 1  0  0  2 0  0  0 0 | 1 0  1  2 2 0 0 0 | 1 1 2 0
oo oo oo6oo&#x |  1  1 | *  * 24  *  *  * | 0 0  1  1  2 0  0  0 0 | 0 1  2  2 1 0 0 0 | 2 1 1 0
.x .. .. ..    |  0  2 | *  *  * 12  *  * | 0 0  1  0  0 1  2  0 0 | 0 1  2  0 0 2 1 0 | 2 1 0 1
.. .x .. ..    |  0  2 | *  *  *  * 12  * | 0 0  0  1  0 1  0  2 0 | 0 1  0  2 0 2 0 1 | 2 0 1 1
.. .. .x ..    |  0  2 | *  *  *  *  * 24 | 0 0  0  0  1 0  1  1 1 | 0 0  1  1 1 1 1 1 | 1 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. x. ..    |  4  0 | 2  2  0  0  0  0 | 6 *  *  *  * *  *  * * | 1 0  0  2 0 0 0 0 | 1 0 2 0
.. .. x.6o.    |  6  0 | 0  6  0  0  0  0 | * 2  *  *  * *  *  * * | 1 0  0  0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x |  1  2 | 0  0  2  1  0  0 | * * 12  *  * *  *  * * | 0 1  2  0 0 0 0 0 | 2 1 0 0
.. xx .. ..&#x |  2  2 | 1  0  2  0  1  0 | * *  * 12  * *  *  * * | 0 1  0  2 0 0 0 0 | 2 0 1 0
.. .. xx ..&#x |  2  2 | 0  1  2  0  0  1 | * *  *  * 24 *  *  * * | 0 0  1  1 1 0 0 0 | 1 1 1 0
.x .x .. ..    |  0  4 | 0  0  0  2  2  0 | * *  *  *  * 6  *  * * | 0 1  0  0 0 2 0 0 | 2 0 0 1
.x .. .x ..    |  0  4 | 0  0  0  2  0  2 | * *  *  *  * * 12  * * | 0 0  1  0 0 1 1 0 | 1 1 0 1
.. .x .x ..    |  0  4 | 0  0  0  0  2  2 | * *  *  *  * *  * 12 * | 0 0  0  1 0 1 0 1 | 1 0 1 1
.. .. .x6.o    |  0  6 | 0  0  0  0  0  6 | * *  *  *  * *  *  * 4 | 0 0  0  0 1 0 1 1 | 0 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. x.6o.    ♦ 12  0 | 6 12  0  0  0  0 | 6 2  0  0  0 0  0  0 0 | 1 *  *  * * * * * | 0 0 2 0
ox xx .. ..&#x ♦  2  4 | 1  0  4  2  2  0 | 0 0  2  2  0 1  0  0 0 | * 6  *  * * * * * | 2 0 0 0
ox .. xx ..&#x ♦  2  4 | 0  1  4  2  0  2 | 0 0  2  0  2 0  1  0 0 | * * 12  * * * * * | 1 1 0 0
.. xx xx ..&#x ♦  4  4 | 2  2  4  0  2  2 | 1 0  0  2  2 0  0  1 0 | * *  * 12 * * * * | 1 0 1 0
.. .. xx6oo&#x ♦  6  6 | 0  6  6  0  0  6 | 0 1  0  0  6 0  0  0 1 | * *  *  * 4 * * * | 0 1 1 0
.x .x .x ..    ♦  0  8 | 0  0  0  4  4  4 | 0 0  0  0  0 2  2  2 0 | * *  *  * * 6 * * | 1 0 0 1
.x .. .x6.o    ♦  0 12 | 0  0  0  6  0 12 | 0 0  0  0  0 0  6  0 2 | * *  *  * * * 2 * | 0 1 0 1
.. .x .x6.o    ♦  0 12 | 0  0  0  0  6 12 | 0 0  0  0  0 0  0  6 2 | * *  *  * * * * 2 | 0 0 1 1
---------------+-------+------------------+------------------------+-------------------+--------
ox xx xx ..&#x ♦  4  8 | 2  2  8  4  4  4 | 1 0  4  4  4 2  2  2 0 | 0 2  2  2 0 1 0 0 | 6 * * *
ox .. xx6oo&#x ♦  6 12 | 0  6 12  6  0 12 | 0 1  6  0 12 0  6  0 2 | 0 0  6  0 2 0 1 0 | * 2 * *
.. xx xx6oo&#x ♦ 12 12 | 6 12 12  0  6 12 | 6 2  0  6 12 0  0  6 2 | 1 0  0  6 2 0 0 1 | * * 2 *
.x .x .x6.o    ♦  0 24 | 0  0  0 12 12 24 | 0 0  0  0  0 6 12 12 4 | 0 0  0  0 0 6 2 2 | * * * 1
```

```ox xx xx3xx&#x   → height = sqrt(3)/2 = 0.866025
(hip || shiddip)

o. o. o.3o.    | 12  * | 1 1 1  2  0  0  0  0 | 1 1 1  1  2  2  2 0 0 0 0 0 0 | 1 1 1 1 2 2 2 0 0 0 0 | 1 1 1 2 0
.o .o .o3.o    |  * 24 | 0 0 0  1  1  1  1  1 | 0 0 0  1  1  1  1 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------------+-------+----------------------+-------------------------------+-----------------------+----------
.. x. .. ..    |  2  0 | 6 * *  *  *  *  *  * | 1 1 0  0  2  0  0 0 0 0 0 0 0 | 1 1 0 0 2 2 0 0 0 0 0 | 1 1 0 2 0
.. .. x. ..    |  2  0 | * 6 *  *  *  *  *  * | 1 0 1  0  0  2  0 0 0 0 0 0 0 | 1 0 1 0 2 0 2 0 0 0 0 | 1 0 1 2 0
.. .. .. x.    |  2  0 | * * 6  *  *  *  *  * | 0 1 1  0  0  0  2 0 0 0 0 0 0 | 1 0 0 1 0 2 2 0 0 0 0 | 0 1 1 2 0
oo oo oo3oo&#x |  1  1 | * * * 24  *  *  *  * | 0 0 0  1  1  1  1 0 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.x .. .. ..    |  0  2 | * * *  * 12  *  *  * | 0 0 0  1  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
.. .x .. ..    |  0  2 | * * *  *  * 12  *  * | 0 0 0  0  1  0  0 1 0 0 1 1 0 | 0 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
.. .. .x ..    |  0  2 | * * *  *  *  * 12  * | 0 0 0  0  0  1  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  2 | * * *  *  *  *  * 12 | 0 0 0  0  0  0  1 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------------+-------+----------------------+-------------------------------+-----------------------+----------
.. x. x. ..    |  4  0 | 2 2 0  0  0  0  0  0 | 3 * *  *  *  *  * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 | 1 0 0 2 0
.. x. .. x.    |  4  0 | 2 0 2  0  0  0  0  0 | * 3 *  *  *  *  * * * * * * * | 1 0 0 0 0 2 0 0 0 0 0 | 0 1 0 2 0
.. .. x.3x.    |  6  0 | 0 3 3  0  0  0  0  0 | * * 2  *  *  *  * * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x |  1  2 | 0 0 0  2  1  0  0  0 | * * * 12  *  *  * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
.. xx .. ..&#x |  2  2 | 1 0 0  2  0  1  0  0 | * * *  * 12  *  * * * * * * * | 0 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
.. .. xx ..&#x |  2  2 | 0 1 0  2  0  0  1  0 | * * *  *  * 12  * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x |  2  2 | 0 0 1  2  0  0  0  1 | * * *  *  *  * 12 * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. ..    |  0  4 | 0 0 0  0  2  2  0  0 | * * *  *  *  *  * 6 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.x .. .x ..    |  0  4 | 0 0 0  0  2  0  2  0 | * * *  *  *  *  * * 6 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.x .. .. .x    |  0  4 | 0 0 0  0  2  0  0  2 | * * *  *  *  *  * * * 6 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
.. .x .x ..    |  0  4 | 0 0 0  0  0  2  2  0 | * * *  *  *  *  * * * * 6 * * | 0 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
.. .x .. .x    |  0  4 | 0 0 0  0  0  2  0  2 | * * *  *  *  *  * * * * * 6 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.. .. .x3.x    |  0  6 | 0 0 0  0  0  0  3  3 | * * *  *  *  *  * * * * * * 4 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+-------+----------------------+-------------------------------+-----------------------+----------
.. x. x.3x.    ♦ 12  0 | 6 6 6  0  0  0  0  0 | 3 3 2  0  0  0  0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 0 0 0 2 0
ox xx .. ..&#x ♦  2  4 | 1 0 0  4  2  2  0  0 | 0 0 0  2  2  0  0 1 0 0 0 0 0 | * 6 * * * * * * * * * | 1 1 0 0 0
ox .. xx ..&#x ♦  2  4 | 0 1 0  4  2  0  2  0 | 0 0 0  2  0  2  0 0 1 0 0 0 0 | * * 6 * * * * * * * * | 1 0 1 0 0
ox .. .. xx&#x ♦  2  4 | 0 0 1  4  2  0  0  2 | 0 0 0  2  0  0  2 0 0 1 0 0 0 | * * * 6 * * * * * * * | 0 1 1 0 0
.. xx xx ..&#x ♦  4  4 | 2 2 0  4  0  2  2  0 | 1 0 0  0  2  2  0 0 0 0 1 0 0 | * * * * 6 * * * * * * | 1 0 0 1 0
.. xx .. xx&#x ♦  4  4 | 2 0 2  4  0  2  0  2 | 0 1 0  0  2  0  2 0 0 0 0 1 0 | * * * * * 6 * * * * * | 0 1 0 1 0
.. .. xx3xx&#x ♦  6  6 | 0 3 3  6  0  0  3  3 | 0 0 1  0  0  3  3 0 0 0 0 0 1 | * * * * * * 4 * * * * | 0 0 1 1 0
.x .x .x ..    ♦  0  8 | 0 0 0  0  4  4  4  0 | 0 0 0  0  0  0  0 2 2 0 2 0 0 | * * * * * * * 3 * * * | 1 0 0 0 1
.x .x .. .x    ♦  0  8 | 0 0 0  0  4  4  0  4 | 0 0 0  0  0  0  0 2 0 2 0 2 0 | * * * * * * * * 3 * * | 0 1 0 0 1
.x .. .x3.x    ♦  0 12 | 0 0 0  0  6  0  6  6 | 0 0 0  0  0  0  0 0 3 3 0 0 2 | * * * * * * * * * 2 * | 0 0 1 0 1
.. .x .x3.x    ♦  0 12 | 0 0 0  0  0  6  6  6 | 0 0 0  0  0  0  0 0 0 0 3 3 2 | * * * * * * * * * * 2 | 0 0 0 1 1
---------------+-------+----------------------+-------------------------------+-----------------------+----------
ox xx xx ..&#x ♦  4  8 | 2 2 0  8  4  4  4  0 | 1 0 0  4  4  4  0 2 2 0 2 0 0 | 0 2 2 0 2 0 0 1 0 0 0 | 3 * * * *
ox xx .. xx&#x ♦  4  8 | 2 0 2  8  4  4  0  4 | 0 1 0  4  4  0  4 2 0 2 0 2 0 | 0 2 0 2 0 2 0 0 1 0 0 | * 3 * * *
ox .. xx3xx&#x ♦  6 12 | 0 3 3 12  6  0  6  6 | 0 0 1  6  0  6  6 0 3 3 0 0 2 | 0 0 3 3 0 0 2 0 0 1 0 | * * 2 * *
.. xx xx3xx&#x ♦ 12 12 | 6 6 6 12  0  6  6  6 | 3 3 2  0  6  6  6 0 0 0 3 3 2 | 1 0 0 0 3 3 2 0 0 0 1 | * * * 2 *
.x .x .x3.x    ♦  0 24 | 0 0 0  0 12 12 12 12 | 0 0 0  0  0  0  0 6 6 6 6 6 4 | 0 0 0 0 0 0 0 3 3 2 2 | * * * * 1
```

```xxx xxx3xxx&#x   → all pairwise heights = 1

o.. o..3o..    | 12  *  * | 1 1 1  1  1 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 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 0
.o. .o.3.o.    |  * 12  * | 0 0 0  1  0 1 1 1  1 0 0 0 | 0 0 0 1 1 1 0 0 0  1 1 1 1 1 1 1 0 0 0 | 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 | 1 0 1 1 1 1
..o ..o3..o    |  *  * 12 | 0 0 0  0  1 0 0 0  1 1 1 1 | 0 0 0 0 0 0 1 1 1  1 0 0 0 1 1 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+----------+----------------------------+----------------------------------------+-------------------------------+------------
x.. ... ...    |  2  0  0 | 6 * *  *  * * * *  * * * * | 1 1 0 1 0 0 1 0 0  0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 1 0 0
... x.. ...    |  2  0  0 | * 6 *  *  * * * *  * * * * | 1 0 1 0 1 0 0 1 0  0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 | 1 1 1 0 1 0
... ... x..    |  2  0  0 | * * 6  *  * * * *  * * * * | 0 1 1 0 0 1 0 0 1  0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 | 1 1 0 1 1 0
oo. oo.3oo.&#x |  1  1  0 | * * * 12  * * * *  * * * * | 0 0 0 1 1 1 0 0 0  1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 | 1 0 1 1 1 0
o.o o.o3o.o&#x |  1  0  1 | * * *  * 12 * * *  * * * * | 0 0 0 0 0 0 1 1 1  1 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 1 1 1 1 0
.x. ... ...    |  0  2  0 | * * *  *  * 6 * *  * * * * | 0 0 0 1 0 0 0 0 0  0 1 1 0 1 0 0 0 0 0 | 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 | 1 0 1 1 0 1
... .x. ...    |  0  2  0 | * * *  *  * * 6 *  * * * * | 0 0 0 0 1 0 0 0 0  0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 | 1 0 1 0 1 1
... ... .x.    |  0  2  0 | * * *  *  * * * 6  * * * * | 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 0 0 0 1 1 0 1 1 0 | 1 0 0 1 1 1
.oo .oo3.oo&#x |  0  1  1 | * * *  *  * * * * 12 * * * | 0 0 0 0 0 0 0 0 0  1 0 0 0 1 1 1 0 0 0 | 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 | 0 0 1 1 1 1
..x ... ...    |  0  0  2 | * * *  *  * * * *  * 6 * * | 0 0 0 0 0 0 1 0 0  0 0 0 0 1 0 0 1 1 0 | 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 | 0 1 1 1 0 1
... ..x ...    |  0  0  2 | * * *  *  * * * *  * * 6 * | 0 0 0 0 0 0 0 1 0  0 0 0 0 0 1 0 1 0 1 | 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 | 0 1 1 0 1 1
... ... ..x    |  0  0  2 | * * *  *  * * * *  * * * 6 | 0 0 0 0 0 0 0 0 1  0 0 0 0 0 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 | 0 1 0 1 1 1
---------------+----------+----------------------------+----------------------------------------+-------------------------------+------------
x.. x.. ...    |  4  0  0 | 2 2 0  0  0 0 0 0  0 0 0 0 | 3 * * * * * * * *  * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
x.. ... x..    |  4  0  0 | 2 0 2  0  0 0 0 0  0 0 0 0 | * 3 * * * * * * *  * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... x..3x..    |  6  0  0 | 0 3 3  0  0 0 0 0  0 0 0 0 | * * 2 * * * * * *  * * * * * * * * * * | 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 | 1 1 0 0 1 0
xx. ... ...&#x |  2  2  0 | 1 0 0  2  0 1 0 0  0 0 0 0 | * * * 6 * * * * *  * * * * * * * * * * | 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
... xx. ...&#x |  2  2  0 | 0 1 0  2  0 0 1 0  0 0 0 0 | * * * * 6 * * * *  * * * * * * * * * * | 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
... ... xx.&#x |  2  2  0 | 0 0 1  2  0 0 0 1  0 0 0 0 | * * * * * 6 * * *  * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
x.x ... ...&#x |  2  0  2 | 1 0 0  0  2 0 0 0  0 1 0 0 | * * * * * * 6 * *  * * * * * * * * * * | 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
... x.x ...&#x |  2  0  2 | 0 1 0  0  2 0 0 0  0 0 1 0 | * * * * * * * 6 *  * * * * * * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... ... x.x&#x |  2  0  2 | 0 0 1  0  2 0 0 0  0 0 0 1 | * * * * * * * * 6  * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | 0 1 0 1 1 0
ooo ooo3ooo&#x |  1  1  1 | 0 0 0  1  1 0 0 0  1 0 0 0 | * * * * * * * * * 12 * * * * * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x. .x. ...    |  0  4  0 | 0 0 0  0  0 2 2 0  0 0 0 0 | * * * * * * * * *  * 3 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1
.x. ... .x.    |  0  4  0 | 0 0 0  0  0 2 0 2  0 0 0 0 | * * * * * * * * *  * * 3 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 0 1 0 1
... .x.3.x.    |  0  6  0 | 0 0 0  0  0 0 3 3  0 0 0 0 | * * * * * * * * *  * * * 2 * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 0 1 1
.xx ... ...&#x |  0  2  2 | 0 0 0  0  0 1 0 0  2 1 0 0 | * * * * * * * * *  * * * * 6 * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 1 1 0 1
... .xx ...&#x |  0  2  2 | 0 0 0  0  0 0 1 0  2 0 1 0 | * * * * * * * * *  * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 | 0 0 1 0 1 1
... ... .xx&#x |  0  2  2 | 0 0 0  0  0 0 0 1  2 0 0 1 | * * * * * * * * *  * * * * * * 6 * * * | 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 1
..x ..x ...    |  0  0  4 | 0 0 0  0  0 0 0 0  0 2 2 0 | * * * * * * * * *  * * * * * * * 3 * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 | 0 1 1 0 0 1
..x ... ..x    |  0  0  4 | 0 0 0  0  0 0 0 0  0 2 0 2 | * * * * * * * * *  * * * * * * * * 3 * | 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 | 0 1 0 1 0 1
... ..x3..x    |  0  0  6 | 0 0 0  0  0 0 0 0  0 0 3 3 | * * * * * * * * *  * * * * * * * * * 2 | 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 | 0 1 0 0 1 1
---------------+----------+----------------------------+----------------------------------------+-------------------------------+------------
x.. x..3x..    ♦ 12  0  0 | 6 6 6  0  0 0 0 0  0 0 0 0 | 3 3 2 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 1 0 0 0 0
xx. xx. ...&#x ♦  4  4  0 | 2 2 0  4  0 2 2 0  0 0 0 0 | 1 0 0 2 2 0 0 0 0  0 1 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 0 1 0 0 0
xx. ... xx.&#x ♦  4  4  0 | 2 0 2  4  0 2 0 2  0 0 0 0 | 0 1 0 2 0 2 0 0 0  0 0 1 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * | 1 0 0 1 0 0
... xx.3xx.&#x ♦  6  6  0 | 0 3 3  6  0 0 3 3  0 0 0 0 | 0 0 1 0 3 3 0 0 0  0 0 0 1 0 0 0 0 0 0 | * * * 2 * * * * * * * * * * * | 1 0 0 0 1 0
x.x x.x ...&#x ♦  4  0  4 | 2 2 0  0  4 0 0 0  0 2 2 0 | 1 0 0 0 0 0 2 2 0  0 0 0 0 0 0 0 1 0 0 | * * * * 3 * * * * * * * * * * | 0 1 1 0 0 0
x.x ... x.x&#x ♦  4  0  4 | 2 0 2  0  4 0 0 0  0 2 0 2 | 0 1 0 0 0 0 2 0 2  0 0 0 0 0 0 0 0 1 0 | * * * * * 3 * * * * * * * * * | 0 1 0 1 0 0
... x.x3x.x&#x ♦  6  0  6 | 0 3 3  0  6 0 0 0  0 0 3 3 | 0 0 1 0 0 0 0 3 3  0 0 0 0 0 0 0 0 0 1 | * * * * * * 2 * * * * * * * * | 0 1 0 0 1 0
xxx ... ...&#x ♦  2  2  2 | 1 0 0  2  2 1 0 0  2 1 0 0 | 0 0 0 1 0 0 1 0 0  2 0 0 0 1 0 0 0 0 0 | * * * * * * * 6 * * * * * * * | 0 0 1 1 0 0
... xxx ...&#x ♦  2  2  2 | 0 1 0  2  2 0 1 0  2 0 1 0 | 0 0 0 0 1 0 0 1 0  2 0 0 0 0 1 0 0 0 0 | * * * * * * * * 6 * * * * * * | 0 0 1 0 1 0
... ... xxx&#x ♦  2  2  2 | 0 0 1  2  2 0 0 1  2 0 0 1 | 0 0 0 0 0 1 0 0 1  2 0 0 0 0 0 1 0 0 0 | * * * * * * * * * 6 * * * * * | 0 0 0 1 1 0
.x. .x.3.x.    ♦  0 12  0 | 0 0 0  0  0 6 6 6  0 0 0 0 | 0 0 0 0 0 0 0 0 0  0 3 3 2 0 0 0 0 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xx .xx ...&#x ♦  0  4  4 | 0 0 0  0  0 2 2 0  4 2 2 0 | 0 0 0 0 0 0 0 0 0  0 1 0 0 2 2 0 1 0 0 | * * * * * * * * * * * 3 * * * | 0 0 1 0 0 1
.xx ... .xx&#x ♦  0  4  4 | 0 0 0  0  0 2 0 2  4 2 0 2 | 0 0 0 0 0 0 0 0 0  0 0 1 0 2 0 2 0 1 0 | * * * * * * * * * * * * 3 * * | 0 0 0 1 0 1
... .xx3.xx&#x ♦  0  6  6 | 0 0 0  0  0 0 3 3  6 0 3 3 | 0 0 0 0 0 0 0 0 0  0 0 0 1 0 3 3 0 0 1 | * * * * * * * * * * * * * 2 * | 0 0 0 0 1 1
..x ..x3..x    ♦  0  0 12 | 0 0 0  0  0 0 0 0  0 6 6 6 | 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * * * * * * 1 | 0 1 0 0 0 1
---------------+----------+----------------------------+----------------------------------------+-------------------------------+------------
xx. xx.3xx.&#x ♦ 12 12  0 | 6 6 6 12  0 6 6 6  0 0 0 0 | 3 3 2 6 6 6 0 0 0  0 3 3 2 0 0 0 0 0 0 | 1 3 3 2 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
x.x x.x3x.x&#x ♦ 12  0 12 | 6 6 6  0 12 0 0 0  0 6 6 6 | 3 3 2 0 0 0 6 6 6  0 0 0 0 0 0 0 3 3 2 | 1 0 0 0 3 3 2 0 0 0 0 0 0 0 1 | * 1 * * * *
xxx xxx ...&#x ♦  4  4  4 | 2 2 0  4  4 2 2 0  4 2 2 0 | 1 0 0 2 2 0 2 2 0  4 1 0 0 2 2 0 1 0 0 | 0 1 0 0 1 0 0 2 2 0 0 1 0 0 0 | * * 3 * * *
xxx ... xxx&#x ♦  4  4  4 | 2 0 2  4  4 2 0 2  4 2 0 2 | 0 1 0 2 0 2 2 0 2  4 0 1 0 2 0 2 0 1 0 | 0 0 1 0 0 1 0 2 0 2 0 0 1 0 0 | * * * 3 * *
... xxx3xxx&#x ♦  6  6  6 | 0 3 3  6  6 0 3 3  6 0 3 3 | 0 0 1 0 3 3 0 3 3  6 0 0 1 0 3 3 0 0 1 | 0 0 0 1 0 0 1 0 3 3 0 0 0 1 0 | * * * * 2 *
.xx .xx3.xx&#x ♦  0 12 12 | 0 0 0  0  0 6 6 6 12 6 6 6 | 0 0 0 0 0 0 0 0 0  0 3 3 2 6 6 6 3 3 2 | 0 0 0 0 0 0 0 0 0 0 1 3 3 2 1 | * * * * * 1
```