Acronym tich Name truncated cubic honeycomb ` © ©   ©` Vertex figure ` ©` Confer general polytopal classes: partial Stott expansions   unit-edged relatives: atich Externallinks

Incidence matrix according to Dynkin symbol

```x4x3o4o   (N → ∞)

. . . . | 6N |  1   4 |  4  4 | 4 1
--------+----+--------+-------+----
x . . . |  2 | 3N   * |  4  0 | 4 0
. x . . |  2 |  * 12N |  1  2 | 2 1
--------+----+--------+-------+----
x4x . . |  8 |  4   4 | 3N  * | 2 0
. x3o . |  3 |  0   3 |  * 8N | 1 1
--------+----+--------+-------+----
x4x3o . ♦ 24 | 12  24 |  6  8 | N *
. x3o4o ♦  6 |  0  12 |  0  8 | * N

snubbed forms: s4x3o4o
```

```x4x3o4/3o   (N → ∞)

. . .   . | 6N |  1   4 |  4  4 | 4 1
----------+----+--------+-------+----
x . .   . |  2 | 3N   * |  4  0 | 4 0
. x .   . |  2 |  * 12N |  1  2 | 2 1
----------+----+--------+-------+----
x4x .   . |  8 |  4   4 | 3N  * | 2 0
. x3o   . |  3 |  0   3 |  * 8N | 1 1
----------+----+--------+-------+----
x4x3o   . ♦ 24 | 12  24 |  6  8 | N *
. x3o4/3o ♦  6 |  0  12 |  0  8 | * N
```

```o3x3o *b4x   (N → ∞)

. . .    . | 12N |   4  1 |  2  2  4 |  1 2 2
-----------+-----+--------+----------+-------
. x .    . |   2 | 24N  * |  1  1  1 |  1 1 1
. . .    x |   2 |   * 6N |  0  0  4 |  0 2 2
-----------+-----+--------+----------+-------
o3x .    . |   3 |   3  0 | 8N  *  * |  1 1 0
. x3o    . |   3 |   3  0 |  * 8N  * |  1 0 1
. x . *b4x |   8 |   4  4 |  *  * 6N |  0 1 1
-----------+-----+--------+----------+-------
o3x3o    . ♦   6 |  12  0 |  4  4  0 | 2N * *
o3x . *b4x ♦  24 |  24 12 |  8  0  6 |  * N *
. x3o *b4x ♦  24 |  24 12 |  0  8  6 |  * * N

snubbed forms: o3x3o *b4s
```

```wx4ox3xo4xw&#zx   (N → ∞)   → height = 0
(tegum sum of 2 inverted (w,x,x)-prichs)

o.4o.3o.4o.     & | 24N |   2   1   2 |  1  2  2   3 | 1  3  1
------------------+-----+-------------+--------------+--------
.. .. x. ..     & |   2 | 24N   *   * |  1  1  0   1 | 1  1  1
.. .. .. x.     & |   2 |   * 12N   * |  0  2  2   0 | 1  3  0
oo4oo3oo4oo&#x    |   2 |   *   * 24N |  0  0  1   2 | 0  2  1
------------------+-----+-------------+--------------+--------
.. o.3x. ..     & |   3 |   3   0   0 | 8N  *  *   * | 1  0  1
.. .. x.4x.     & |   8 |   4   4   0 |  * 6N  *   * | 1  1  0
wx .. .. xw&#zx   |   8 |   0   4   4 |  *  * 6N   * | 0  2  0
.. ox .. ..&#x  & |   3 |   1   0   2 |  *  *  * 24N | 0  1  1
------------------+-----+-------------+--------------+--------
.. o.3x.4x.     & ♦  24 |  24  12   0 |  8  6  0   0 | N  *  *
wx4ox .. xw&#zx & ♦  24 |   8  12  16 |  0  2  4   8 | * 3N  *
.. ox3xo ..&#x    ♦   6 |   6   0   6 |  2  0  0   6 | *  * 4N
```

```:wxw:4:oxo:4:ooo:&##x   (N → ∞)   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
height(3,1') = 1

o.. 4 o.. 4 o..      | N  * * |  4 1  0  0  0 |  4  4 0  0 | 1 4
.o. 4 .o. 4 .o.      | * 4N * |  1 0  1  2  1 |  2  2 2  2 | 1 4
..o 4 ..o 4 ..o      | *  * N |  0 1  0  0  4 |  0  4 0  4 | 1 4
----------------------+--------+---------------+------------+----
oo. 4 oo. 4 oo. &#x  | 1  1 0 | 4N *  *  *  * |  2  1 0  0 | 1 2
:o.o:4:o.o:4:o.o:&#x  | 1  0 1 |  * N  *  *  * |  0  4 0  0 | 0 4
.x.   ...   ...      | 0  2 0 |  * * 2N  *  * |  0  2 2  0 | 0 4
...   .x.   ...      | 0  2 0 |  * *  * 4N  * |  1  0 1  1 | 1 2
.oo 4 .oo 4 .oo &#x  | 0  1 1 |  * *  *  * 4N |  0  1 0  2 | 1 2
----------------------+--------+---------------+------------+----
...   ox.   ... &#x  | 1  2 0 |  2 0  0  1  0 | 4N  * *  * | 1 1
:wxw:  ...   ... &#xt | 2  4 2 |  2 2  2  0  2 |  * 2N *  * | 0 2
.x. 4 .x.   ...      | 0  8 0 |  0 0  4  4  0 |  *  * N  * | 0 2
...   .xo   ... &#x  | 0  2 1 |  0 0  0  1  2 |  *  * * 4N | 1 1
----------------------+--------+---------------+------------+----
...   oxo 4 ooo &#xt ♦ 1  4 1 |  4 0  0  4  4 |  4  0 0  4 | N *
:wxw:4:oxo:  ... &#xt ♦ 4 16 4 |  8 4  8  8  8 |  4  4 2  4 | * N
```

```:ooxwwx:3:xwwxoo:3:wxooxw:3*a&##x   (N → ∞)   → height(1,2) = height(3,4) = height(5,6) = 1/sqrt(3) = 0.577350
height(2,3) = height(4,5) = height(6,1') = sqrt(2/3) = 0.816497

o..... 3 o..... 3 o..... 3*a     | 3N  *  *  *  *  * |  2  1  0  0  0  0  0  0  0  0  0  2 | 1  2 0  0  0 0  0 0  0  0 0  2 0  1  2 | 1 1 2 0 0 1
.o.... 3 .o.... 3 .o.... 3*a     |  * 3N  *  *  *  * |  0  1  2  2  0  0  0  0  0  0  0  0 | 0  2 1  1  2 0  0 0  0  0 0  2 0  0  0 | 1 1 2 1 0 0
..o... 3 ..o... 3 ..o... 3*a     |  *  * 3N  *  *  * |  0  0  0  2  2  1  0  0  0  0  0  0 | 0  2 0  2  1 1  2 0  0  0 0  0 0  0  0 | 2 1 1 1 0 0
...o.. 3 ...o.. 3 ...o.. 3*a     |  *  *  * 3N  *  * |  0  0  0  0  0  1  2  2  0  0  0  0 | 0  2 0  0  0 0  2 1  2  1 0  0 0  0  0 | 2 1 1 0 1 0
....o. 3 ....o. 3 ....o. 3*a     |  *  *  *  * 3N  * |  0  0  0  0  0  0  0  2  2  1  0  0 | 0  0 0  0  0 0  2 0  1  2 1  2 0  0  0 | 1 2 1 0 1 0
.....o 3 .....o 3 .....o 3*a     |  *  *  *  *  * 3N |  0  0  0  0  0  0  0  0  0  1  2  2 | 0  0 0  0  0 0  2 0  0  0 0  2 1  2  1 | 1 2 1 0 0 1
----------------------------------+-------------------+-------------------------------------+----------------------------------------+------------
......   x.....   ......         |  2  0  0  0  0  0 | 3N  *  *  *  *  *  *  *  *  *  *  * | 1  1 0  0  0 0  0 0  0  0 0  0 0  0  1 | 1 0 1 0 0 1
oo.... 3 oo.... 3 oo.... 3*a&#x  |  1  1  0  0  0  0 |  * 3N  *  *  *  *  *  *  *  *  *  * | 0  2 0  0  0 0  0 0  0  0 0  2 0  0  0 | 1 1 2 0 0 0
......   ......   .x....         |  0  2  0  0  0  0 |  *  * 3N  *  *  *  *  *  *  *  *  * | 0  0 1  0  1 0  0 0  0  0 0  1 0  0  0 | 0 1 1 1 0 0
.oo... 3 .oo... 3 .oo... 3*a&#x  |  0  1  1  0  0  0 |  *  *  * 6N  *  *  *  *  *  *  *  * | 0  1 0  1  1 0  0 0  0  0 0  0 0  0  0 | 1 0 1 1 0 0
..x...   ......   ......         |  0  0  2  0  0  0 |  *  *  *  * 3N  *  *  *  *  *  *  * | 0  0 0  1  0 1  1 0  0  0 0  0 0  0  0 | 1 1 0 1 0 0
..oo.. 3 ..oo.. 3 ..oo.. 3*a&#x  |  0  0  1  1  0  0 |  *  *  *  *  * 3N  *  *  *  *  *  * | 0  2 0  0  0 0  2 0  0  0 0  0 0  0  0 | 2 1 1 0 0 0
......   ...x..   ......         |  0  0  0  2  0  0 |  *  *  *  *  *  * 3N  *  *  *  *  * | 0  1 0  0  0 0  0 1  1  0 0  0 0  0  0 | 1 0 1 0 1 0
...oo. 3 ...oo. 3 ...oo. 3*a&#x  |  0  0  0  1  1  0 |  *  *  *  *  *  *  * 6N  *  *  *  * | 0  0 0  0  0 0  1 0  1  1 0  0 0  0  0 | 1 1 0 0 1 0
......   ......   ....x.         |  0  0  0  0  2  0 |  *  *  *  *  *  *  *  * 3N  *  *  * | 0  0 0  0  0 0  0 0  0  1 1  1 0  0  0 | 0 1 1 0 1 0
....oo 3 ....oo 3 ....oo 3*a&#x  |  0  0  0  0  1  1 |  *  *  *  *  *  *  *  *  * 3N  *  * | 0  0 0  0  0 0  2 0  0  0 0  2 0  0  0 | 1 2 1 0 0 0
.....x   ......   ......         |  0  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 3N  * | 0  0 0  0  0 0  1 0  0  0 0  0 1  1  0 | 1 1 0 0 0 1
:o....o:3:o....o:3:o....o:3*a&#x  |  1  0  0  0  0  1 |  *  *  *  *  *  *  *  *  *  *  * 6N | 0  0 0  0  0 0  0 0  0  0 0  1 0  1  1 | 0 1 1 0 0 1
----------------------------------+-------------------+-------------------------------------+----------------------------------------+------------
o..... 3 x.....   ......         |  3  0  0  0  0  0 |  3  0  0  0  0  0  0  0  0  0  0  0 | N  * *  *  * *  * *  *  * *  * *  *  * | 1 0 0 0 0 1
......   xwwx..   ......    &#xt |  2  2  2  2  0  0 |  1  2  0  2  0  2  1  0  0  0  0  0 | * 3N *  *  * *  * *  *  * *  * *  *  * | 1 0 1 0 0 0
.o....   ......   .x.... 3*a     |  0  3  0  0  0  0 |  0  0  3  0  0  0  0  0  0  0  0  0 | *  * N  *  * *  * *  *  * *  * *  *  * | 0 1 0 1 0 0
.ox...   ......   ......    &#x  |  0  1  2  0  0  0 |  0  0  0  2  1  0  0  0  0  0  0  0 | *  * * 3N  * *  * *  *  * *  * *  *  * | 1 0 0 1 0 0
......   ......   .xo...    &#x  |  0  2  1  0  0  0 |  0  0  1  2  0  0  0  0  0  0  0  0 | *  * *  * 3N *  * *  *  * *  * *  *  * | 0 0 1 1 0 0
..x...   ......   ..o... 3*a     |  0  0  3  0  0  0 |  0  0  0  0  3  0  0  0  0  0  0  0 | *  * *  *  * N  * *  *  * *  * *  *  * | 0 1 0 1 0 0
..xwwx   ......   ......    &#xt |  0  0  2  2  2  2 |  0  0  0  0  1  2  0  2  0  2  1  0 | *  * *  *  * * 3N *  *  * *  * *  *  * | 1 1 0 0 0 0
......   ...x.. 3 ...o..         |  0  0  0  3  0  0 |  0  0  0  0  0  0  3  0  0  0  0  0 | *  * *  *  * *  * N  *  * *  * *  *  * | 0 0 1 0 1 0
......   ...xo.   ......    &#x  |  0  0  0  2  1  0 |  0  0  0  0  0  0  1  2  0  0  0  0 | *  * *  *  * *  * * 3N  * *  * *  *  * | 1 0 0 0 1 0
......   ......   ...ox.    &#x  |  0  0  0  1  2  0 |  0  0  0  0  0  0  0  2  1  0  0  0 | *  * *  *  * *  * *  * 3N *  * *  *  * | 0 1 0 0 1 0
......   ....o. 3 ....x.         |  0  0  0  0  3  0 |  0  0  0  0  0  0  0  0  3  0  0  0 | *  * *  *  * *  * *  *  * N  * *  *  * | 0 0 1 0 1 0
......   ......  :wx..xw:   &#xt |  2  2  0  0  2  2 |  0  2  1  0  0  0  0  0  1  2  0  2 | *  * *  *  * *  * *  *  * * 3N *  *  * | 0 1 1 0 0 0
.....x 3 .....o   ......         |  0  0  0  0  0  3 |  0  0  0  0  0  0  0  0  0  0  3  0 | *  * *  *  * *  * *  *  * *  * N  *  * | 1 0 0 0 0 1
:o....x:  ......   ......    &#x  |  1  0  0  0  0  2 |  0  0  0  0  0  0  0  0  0  0  1  2 | *  * *  *  * *  * *  *  * *  * * 3N  * | 0 1 0 0 0 1
......  :x....o:  ......    &#x  |  2  0  0  0  0  1 |  1  0  0  0  0  0  0  0  0  0  0  2 | *  * *  *  * *  * *  *  * *  * *  * 3N | 0 0 1 0 0 1
----------------------------------+-------------------+-------------------------------------+----------------------------------------+------------
ooxwwx 3 xwwxoo   ......    &#xt ♦  3  3  6  6  3  3 |  3  3  0  6  3  6  3  6  0  3  3  0 | 1  3 0  3  0 0  3 0  3  0 0  0 1  0  0 | N * * * * *
:ooxwwx:  ......  :wxooxw:3*a&#xt ♦  3  3  3  3  6  6 |  0  3  3  0  3  3  0  6  3  6  3  6 | 0  0 1  0  0 1  3 0  0  3 0  3 0  3  0 | * N * * * *
......  :xwwxoo:3:wxooxw:   &#xt ♦  6  6  3  3  3  3 |  3  6  3  6  0  3  3  0  3  3  0  6 | 0  3 0  0  3 0  0 1  0  0 1  3 0  0  3 | * * N * * *
.ox...   ......   .xo... 3*a&#x  ♦  0  3  3  0  0  0 |  0  0  3  6  3  0  0  0  0  0  0  0 | 0  0 1  3  3 1  0 0  0  0 0  0 0  0  0 | * * * N * *
......   ...xo. 3 ...ox.    &#x  ♦  0  0  0  3  3  0 |  0  0  0  0  0  0  3  6  3  0  0  0 | 0  0 0  0  0 0  0 1  3  3 1  0 0  0  0 | * * * * N *
:o....x:3:x....o:  ......    &#x  ♦  3  0  0  0  0  3 |  3  0  0  0  0  0  0  0  0  0  3  6 | 1  0 0  0  0 0  0 0  0  0 0  0 1  3  3 | * * * * * N
```