Acronym grich Name great rhombated cubic honeycomb,cantitruncated cubic honeycomb ` © ©   ©` Vertex figure ` ©` Confer general polytopal classes: partial Stott expansions Externallinks

As abstract polytope grich is isomorphic to gaqrich, thereby replacing octagons by octagrams, resp. girco by quitco.

Incidence matrix according to Dynkin symbol

```x4x3x4o   (N → ∞)

. . . . | 24N |   1   1   2 |  1   2  2  1 | 2  1 1
--------+-----+-------------+--------------+-------
x . . . |   2 | 12N   *   * |  1   2  0  0 | 2  1 0
. x . . |   2 |   * 12N   * |  1   0  2  0 | 2  0 1
. . x . |   2 |   *   * 24N |  0   1  1  1 | 1  1 1
--------+-----+-------------+--------------+-------
x4x . . |   8 |   4   4   0 | 3N   *  *  * | 2  0 0
x . x . |   4 |   2   0   2 |  * 12N  *  * | 1  1 0
. x3x . |   6 |   0   3   3 |  *   * 8N  * | 1  0 1
. . x4o |   4 |   0   0   4 |  *   *  * 6N | 0  1 1
--------+-----+-------------+--------------+-------
x4x3x . ♦  48 |  24  24  24 |  6  12  8  0 | N  * *
x . x4o ♦   8 |   4   0   8 |  0   4  0  2 | * 3N *
. x3x4o ♦  24 |   0  12  24 |  0   0  8  6 | *  * N

snubbed forms: s4x3x4o, x4s3s4o, s4s3s4o
```

```x4x3x4/3o   (N → ∞)

. . .   . | 24N |   1   1   2 |  1   2  2  1 | 2  1 1
----------+-----+-------------+--------------+-------
x . .   . |   2 | 12N   *   * |  1   2  0  0 | 2  1 0
. x .   . |   2 |   * 12N   * |  1   0  2  0 | 2  0 1
. . x   . |   2 |   *   * 24N |  0   1  1  1 | 1  1 1
----------+-----+-------------+--------------+-------
x4x .   . |   8 |   4   4   0 | 3N   *  *  * | 2  0 0
x . x   . |   4 |   2   0   2 |  * 12N  *  * | 1  1 0
. x3x   . |   6 |   0   3   3 |  *   * 8N  * | 1  0 1
. . x4/3o |   4 |   0   0   4 |  *   *  * 6N | 0  1 1
----------+-----+-------------+--------------+-------
x4x3x   . ♦  48 |  24  24  24 |  6  12  8  0 | N  * *
x . x4/3o ♦   8 |   4   0   8 |  0   4  0  2 | * 3N *
. x3x4/3o ♦  24 |   0  12  24 |  0   0  8  6 | *  * N
```

```x3x3x *b4x   (N → ∞)

. . .    . | 48N |   1   1   1   1 |  1   1   1  1  1   1 |  1 1  1 1
-----------+-----+-----------------+----------------------+----------
x . .    . |   2 | 24N   *   *   * |  1   1   1  0  0   0 |  1 1  1 0
. x .    . |   2 |   * 24N   *   * |  1   0   0  1  1   0 |  1 1  0 1
. . 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
-----------+-----+-----------------+----------------------+----------
x3x .    . |   6 |   3   3   0   0 | 8N   *   *  *  *   * |  1 1  0 0
x . x    . |   4 |   2   0   2   0 |  * 12N   *  *  *   * |  1 0  1 0
x . .    x |   4 |   2   0   0   2 |  *   * 12N  *  *   * |  0 1  1 0
. x3x    . |   6 |   0   3   3   0 |  *   *   * 8N  *   * |  1 0  0 1
. x . *b4x |   8 |   0   4   0   4 |  *   *   *  * 6N   * |  0 1  0 1
. . x    x |   4 |   0   0   2   2 |  *   *   *  *  * 12N |  0 0  1 1
-----------+-----+-----------------+----------------------+----------
x3x3x    . ♦  24 |  12  12  12   0 |  4   6   0  4  0   0 | 2N *  * *
x3x . *b4x ♦  48 |  24  24   0  24 |  8   0  12  0  6   0 |  * N  * *
x . x    x ♦   8 |   4   0   4   4 |  0   2   2  0  0   2 |  * * 6N *
. x3x *b4x ♦  48 |   0  24  24  24 |  0   0   0  8  6  12 |  * *  * N

snubbed forms: s3s3s *b4x, s3s3s *b4s
```

```s4x3x4x   (N → ∞)

demi( . . . . ) | 48N |   1   1   1   1 |  1   1  1   1  1   1 | 1  1  1 1
----------------+-----+-----------------+----------------------+----------
demi( . x . . ) |   2 | 24N   *   *   * |  1   1  0   1  0   0 | 1  1  1 0
demi( . . x . ) |   2 |   * 24N   *   * |  1   0  1   0  1   0 | 1  1  0 1
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( . x3x . ) |   6 |   3   3   0   0 | 8N   *  *   *  *   * | 1  1  0 0
demi( . x . x ) |   4 |   2   0   2   0 |  * 12N  *   *  *   * | 1  0  1 0
demi( . . x4x ) |   8 |   0   4   4   0 |  *   * 6N   *  *   * | 1  0  0 1
s4x . .   |   4 |   2   0   0   2 |  *   *  * 12N  *   * | 0  1  1 0
sefa( s4x3x . ) |   6 |   0   3   0   3 |  *   *  *   * 8N   * | 0  1  0 1
sefa( s4x . x ) |   4 |   0   0   2   2 |  *   *  *   *  * 12N | 0  0  1 1
----------------+-----+-----------------+----------------------+----------
demi( . x3x4x ) ♦  48 |  24  24  24   0 |  8  12  6   0  0   0 | N  *  * *
s4x3x .   ♦  24 |  12  12   0  12 |  4   0  0   6  4   0 | * 2N  * *
s4x . x   ♦   8 |   4   0   4   4 |  0   2  0   2  0   2 | *  * 6N *
sefa( s4x3x4x ) ♦  48 |   0  24  24  24 |  0   0  6   0  8  12 | *  *  * N

starting figure: x4x3x4x
```

```:wxxxw:4:xuxux:4:ooqoo:&##x   (N → ∞)   → height(1,2) = height(2,3) = height(3,4) = height(4,5) = 1/sqrt(2) = 0.707107
height(5,1') = 1

o.... 4 o.... 4 o....      | 4N  *  *  *  * |  2  1  0  0  0  0  0  0  0  0  1 | 1  2  0  0 0  0  0 0  1  2 | 1  0 2 1
.o... 4 .o... 4 .o...      |  * 4N  *  *  * |  0  1  1  2  0  0  0  0  0  0  0 | 0  2  2  1 0  0  0 0  1  0 | 1  1 2 0
..o.. 4 ..o.. 4 ..o..      |  *  * 8N  *  * |  0  0  0  1  1  1  1  0  0  0  0 | 0  1  1  1 1  1  1 0  0  0 | 1  1 2 0
...o. 4 ...o. 4 ...o.      |  *  *  * 4N  * |  0  0  0  0  0  0  2  1  1  0  0 | 0  0  0  1 0  2  2 0  1  0 | 1  1 2 0
....o 4 ....o 4 ....o      |  *  *  *  * 4N |  0  0  0  0  0  0  0  0  1  2  1 | 0  0  0  0 0  0  2 1  1  2 | 1  0 2 1
----------------------------+----------------+----------------------------------+----------------------------+---------
.....   x....   .....      |  2  0  0  0  0 | 4N  *  *  *  *  *  *  *  *  *  * | 1  1  0  0 0  0  0 0  0  1 | 1  0 1 1
oo... 4 oo... 4 oo... &#x  |  1  1  0  0  0 |  * 4N  *  *  *  *  *  *  *  *  * | 0  2  0  0 0  0  0 0  1  0 | 1  0 2 0
.x...   .....   .....      |  0  2  0  0  0 |  *  * 2N  *  *  *  *  *  *  *  * | 0  0  2  0 0  0  0 0  1  0 | 0  1 2 0
.oo.. 4 .oo.. 4 .oo.. &#x  |  0  1  1  0  0 |  *  *  * 8N  *  *  *  *  *  *  * | 0  1  1  1 0  0  0 0  0  0 | 1  1 1 0
..x..   .....   .....      |  0  0  2  0  0 |  *  *  *  * 4N  *  *  *  *  *  * | 0  0  1  0 1  1  0 0  0  0 | 0  1 2 0
.....   ..x..   .....      |  0  0  2  0  0 |  *  *  *  *  * 4N  *  *  *  *  * | 0  1  0  0 1  0  1 0  0  0 | 1  0 2 0
..oo. 4 ..oo. 4 ..oo. &#x  |  0  0  1  1  0 |  *  *  *  *  *  * 8N  *  *  *  * | 0  0  0  1 0  1  1 0  0  0 | 1  1 1 0
...x.   .....   .....      |  0  0  0  2  0 |  *  *  *  *  *  *  * 2N  *  *  * | 0  0  0  0 0  2  0 0  1  0 | 0  1 2 0
...oo 4 ...oo 4 ...oo &#x  |  0  0  0  1  1 |  *  *  *  *  *  *  *  * 4N  *  * | 0  0  0  0 0  0  2 0  1  0 | 1  0 2 0
.....   ....x   .....      |  0  0  0  0  2 |  *  *  *  *  *  *  *  *  * 4N  * | 0  0  0  0 0  0  1 1  0  1 | 1  0 1 1
:o...o:4:o...o:4:o...o:&#x  |  1  0  0  0  1 |  *  *  *  *  *  *  *  *  *  * 4N | 0  0  0  0 0  0  0 0  1  2 | 0  0 2 1
----------------------------+----------------+----------------------------------+----------------------------+---------
.....   x.... 4 o....      |  4  0  0  0  0 |  4  0  0  0  0  0  0  0  0  0  0 | N  *  *  * *  *  * *  *  * | 1  0 0 1
.....   xux..   ..... &#xt |  2  2  2  0  0 |  1  2  0  2  0  1  0  0  0  0  0 | * 4N  *  * *  *  * *  *  * | 1  0 1 0
.xx..   .....   ..... &#x  |  0  2  2  0  0 |  0  0  1  2  1  0  0  0  0  0  0 | *  * 4N  * *  *  * *  *  * | 0  1 1 0
.....   .....   .oqo. &#xt |  0  1  2  1  0 |  0  0  0  2  0  0  2  0  0  0  0 | *  *  * 4N *  *  * *  *  * | 1  1 0 0
..x.. 4 ..x..   .....      |  0  0  8  0  0 |  0  0  0  0  4  4  0  0  0  0  0 | *  *  *  * N  *  * *  *  * | 0  0 2 0
..xx.   .....   ..... &#x  |  0  0  2  2  0 |  0  0  0  0  1  0  2  1  0  0  0 | *  *  *  * * 4N  * *  *  * | 0  1 1 0
.....   ..xux   ..... &#xt |  0  0  2  2  2 |  0  0  0  0  0  1  2  0  2  1  0 | *  *  *  * *  * 4N *  *  * | 1  0 1 0
.....   ....x 4 ....o      |  0  0  0  0  4 |  0  0  0  0  0  0  0  0  0  4  0 | *  *  *  * *  *  * N  *  * | 1  0 0 1
:wx.xw:  .....   ..... &#xt |  2  2  0  2  2 |  0  2  1  0  0  0  0  1  2  0  2 | *  *  *  * *  *  * * 2N  * | 0  0 2 0
.....  :x...x:  ..... &#x  |  2  0  0  0  2 |  1  0  0  0  0  0  0  0  0  1  2 | *  *  *  * *  *  * *  * 4N | 0  0 1 1
----------------------------+----------------+----------------------------------+----------------------------+---------
.....   xuxux 4 ooqoo &#xt ♦  4  4  8  4  4 |  4  4  0  8  0  4  8  0  4  4  0 | 1  4  0  4 0  0  4 1  0  0 | N  * * *
.xxx.   .....   .oqo. &#xt ♦  0  2  4  2  0 |  0  0  1  4  2  0  4  1  0  0  0 | 0  0  2  2 0  2  0 0  0  0 | * 2N * *
:wxxxw:4:xuxux:  ..... &#xt ♦  8  8 16  8  8 |  4  8  4  8  8  8  8  4  8  4  8 | 0  4  4  0 2  4  4 0  4  4 | *  * N *
.....  :x...x:4:o...o:&#x  ♦  4  0  0  0  4 |  4  0  0  0  0  0  0  0  0  4  4 | 1  0  0  0 0  0  0 1  0  4 | *  * * N
```