Acronym srich Name small rhombated cubic honeycomb,cantellated cubic honeycomb ` © ©   ©` Vertex figure ` ©` Confer general polytopal classes: partial Stott expansions Externallinks

Incidence matrix according to Dynkin symbol

```x4o3x4o   (N → ∞)

. . . . | 12N |   2   4 |  1   4  2  2 | 2  2 1
--------+-----+---------+--------------+-------
x . . . |   2 | 12N   * |  1   2  0  0 | 2  1 0
. . x . |   2 |   * 24N |  0   1  1  1 | 1  1 1
--------+-----+---------+--------------+-------
x4o . . |   4 |   4   0 | 3N   *  *  * | 2  0 0
x . x . |   4 |   2   2 |  * 12N  *  * | 1  1 0
. o3x . |   3 |   0   3 |  *   * 8N  * | 1  0 1
. . x4o |   4 |   0   4 |  *   *  * 6N | 0  1 1
--------+-----+---------+--------------+-------
x4o3x . ♦  24 |  24  24 |  6  12  8  0 | N  * *
x . x4o ♦   8 |   4   8 |  0   4  0  2 | * 3N *
. o3x4o ♦  12 |   0  24 |  0   0  8  6 | *  * N

snubbed forms: s4o3x4o
```

```x4o3x4/3o   (N → ∞)

. . .   . | 12N |   2   4 |  1   4  2  2 | 2  2 1
----------+-----+---------+--------------+-------
x . .   . |   2 | 12N   * |  1   2  0  0 | 2  1 0
. . x   . |   2 |   * 24N |  0   1  1  1 | 1  1 1
----------+-----+---------+--------------+-------
x4o .   . |   4 |   4   0 | 3N   *  *  * | 2  0 0
x . x   . |   4 |   2   2 |  * 12N  *  * | 1  1 0
. o3x   . |   3 |   0   3 |  *   * 8N  * | 1  0 1
. . x4/3o |   4 |   0   4 |  *   *  * 6N | 0  1 1
----------+-----+---------+--------------+-------
x4o3x   . ♦  24 |  24  24 |  6  12  8  0 | N  * *
x . x4/3o ♦   8 |   4   8 |  0   4  0  2 | * 3N *
. o3x4/3o ♦  12 |   0  24 |  0   0  8  6 | *  * N
```

```x3o3x *b4x   (N → ∞)

. . .    . | 24N |   2   2   2 |  1   2   2  1  1   2 |  1 1  2 1
-----------+-----+-------------+----------------------+----------
x . .    . |   2 | 24N   *   * |  1   1   1  0  0   0 |  1 1  1 0
. . x    . |   2 |   * 24N   * |  0   1   0  1  0   1 |  1 0  1 1
. . .    x |   2 |   *   * 24N |  0   0   1  0  1   1 |  0 1  1 1
-----------+-----+-------------+----------------------+----------
x3o .    . |   3 |   3   0   0 | 8N   *   *  *  *   * |  1 1  0 0
x . x    . |   4 |   2   2   0 |  * 12N   *  *  *   * |  1 0  1 0
x . .    x |   4 |   2   0   2 |  *   * 12N  *  *   * |  0 1  1 0
. o3x    . |   3 |   0   3   0 |  *   *   * 8N  *   * |  1 0  0 1
. o . *b4x |   4 |   0   0   4 |  *   *   *  * 6N   * |  0 1  0 1
. . x    x |   4 |   0   2   2 |  *   *   *  *  * 12N |  0 0  1 1
-----------+-----+-------------+----------------------+----------
x3o3x    . ♦  12 |  12  12   0 |  4   6   0  4  0   0 | 2N *  * *
x3o . *b4x ♦  24 |  24   0  24 |  8   0  12  0  6   0 |  * N  * *
x . x    x ♦   8 |   4   4   4 |  0   2   2  0  0   2 |  * * 6N *
. o3x *b4x ♦  24 |   0  24  24 |  0   0   0  8  6  12 |  * *  * N
```

```s4x3o4x   (N → ∞)

demi( . . . . ) | 24N |   2   2   2 |  1   2  1   2  1   2 | 1  1  2 1
----------------+-----+-------------+----------------------+----------
demi( . x . . ) |   2 | 24N   *   * |  1   1  0   1  0   0 | 1  1  1 0
demi( . . . x ) |   2 |   * 24N   * |  0   1  1   0  0   1 | 1  0  1 1
sefa( s4x . . ) |   2 |   *   * 24N |  0   0  0   1  1   1 | 0  1  1 1
----------------+-----+-------------+----------------------+----------
demi( . x3o . ) |   3 |   3   0   0 | 8N   *  *   *  *   * | 1  1  0 0
demi( . x . x ) |   4 |   2   2   0 |  * 12N  *   *  *   * | 1  0  1 0
demi( . . o4x ) |   4 |   0   4   0 |  *   * 6N   *  *   * | 1  0  0 1
s4x . .   |   4 |   2   0   2 |  *   *  * 12N  *   * | 0  1  1 0
sefa( s4x3o . ) |   3 |   0   0   3 |  *   *  *   * 8N   * | 0  1  0 1
sefa( s4x . x ) |   4 |   0   2   2 |  *   *  *   *  * 12N | 0  0  1 1
----------------+-----+-------------+----------------------+----------
demi( . x3o4x ) ♦  24 |  24  24   0 |  8  12  6   0  0   0 | N  *  * *
s4x3o .   ♦  12 |  12   0  12 |  4   0  0   6  4   0 | * 2N  * *
s4x . x   ♦   8 |   4   4   4 |  0   2  0   2  0   2 | *  * 6N *
sefa( s4x3o4x ) ♦  24 |   0  24  24 |  0   0  6   0  8  12 | *  *  * N

starting figure: x4x3o4x
```

```:xxx:4:xox:4:oqo:&##x   (N → ∞)   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
height(3,1') = 1

o.. 4 o.. 4 o..      | 4N  *  * |  1  2  2  0  0  0  0  1 | 1  2  2  1 0  0  0 0  1  2 |  1 1 2 1
.o. 4 .o. 4 .o.      |  * 4N  * |  0  0  2  2  2  0  0  0 | 0  2  1  2 1  2  1 0  0  0 |  2 1 2 0
..o 4 ..o 4 ..o      |  *  * 4N |  0  0  0  0  2  1  2  1 | 0  0  0  1 0  2  2 1  1  2 |  1 1 2 1
----------------------+----------+-------------------------+----------------------------+---------
x..   ...   ...      |  2  0  0 | 2N  *  *  *  *  *  *  * | 0  2  0  0 0  0  0 0  1  0 |  1 0 2 0
...   x..   ...      |  2  0  0 |  * 4N  *  *  *  *  *  * | 1  0  1  0 0  0  0 0  0  1 |  0 1 1 1
oo. 4 oo. 4 oo. &#x  |  1  1  0 |  *  * 8N  *  *  *  *  * | 0  1  1  1 0  0  0 0  0  0 |  1 1 1 0
.x.   ...   ...      |  0  2  0 |  *  *  * 4N  *  *  *  * | 0  1  0  0 1  1  0 0  0  0 |  1 0 2 0
.oo 4 .oo 4 .oo &#x  |  0  1  1 |  *  *  *  * 8N  *  *  * | 0  0  0  1 0  1  1 0  0  0 |  1 1 1 0
..x   ...   ...      |  0  0  2 |  *  *  *  *  * 2N  *  * | 0  0  0  0 0  2  0 0  1  0 |  1 0 2 0
...   ..x   ...      |  0  0  2 |  *  *  *  *  *  * 4N  * | 0  0  0  0 0  0  1 1  0  1 |  0 1 1 1
:o.o:4:o.o:4:o.o:&#x  |  1  0  1 |  *  *  *  *  *  *  * 4N | 0  0  0  0 0  0  0 0  1  2 |  0 0 2 1
----------------------+----------+-------------------------+----------------------------+---------
...   x.. 4 o..      |  4  0  0 |  0  4  0  0  0  0  0  0 | N  *  *  * *  *  * *  *  * |  0 1 0 1
xx.   ...   ... &#x  |  2  2  0 |  1  0  2  1  0  0  0  0 | * 4N  *  * *  *  * *  *  * |  1 0 1 0
...   xo.   ... &#x  |  2  1  0 |  0  1  2  0  0  0  0  0 | *  * 4N  * *  *  * *  *  * |  0 1 1 0
...   ...   oqo &#xt |  1  2  1 |  0  0  2  0  2  0  0  0 | *  *  * 4N *  *  * *  *  * |  1 1 0 0
.x. 4 .o.   ...      |  0  4  0 |  0  0  0  4  0  0  0  0 | *  *  *  * N  *  * *  *  * |  0 0 2 0
.xx   ...   ... &#x  |  0  2  2 |  0  0  0  1  2  1  0  0 | *  *  *  * * 4N  * *  *  * |  1 0 1 0
...   .ox   ... &#x  |  0  1  2 |  0  0  0  0  2  0  1  0 | *  *  *  * *  * 4N *  *  * |  0 1 1 0
...   ..x 4 ..o      |  0  0  4 |  0  0  0  0  0  0  4  0 | *  *  *  * *  *  * N  *  * |  0 1 0 1
:x.x:  ...   ... &#x  |  2  0  2 |  1  0  0  0  0  1  0  2 | *  *  *  * *  *  * * 2N  * |  0 0 2 0
...  :x.x:  ... &#x  |  2  0  2 |  0  1  0  0  0  0  1  2 | *  *  *  * *  *  * *  * 4N |  0 0 1 1
----------------------+----------+-------------------------+----------------------------+---------
xxx   ...   oqo &#xt ♦  2  4  2 |  1  0  4  2  4  1  0  0 | 0  2  0  2 0  2  0 0  0  0 | 2N * * *
...   xox 4 oqo &#xt ♦  4  4  4 |  0  4  8  0  8  0  4  0 | 1  0  4  4 0  0  4 1  0  0 |  * N * *
:xxx:4:xox:  ... &#xt ♦  8  8  8 |  4  4  8  8  8  4  4  8 | 0  4  4  0 2  4  4 0  4  4 |  * * N *
...  :x.x:4:o.o:&#x  ♦  4  0  4 |  0  4  0  0  0  0  4  4 | 1  0  0  0 0  0  0 1  0  4 |  * * * N
```