Acronym otch
Name omnitruncated cubic honeycomb
 
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As abstract polytope otch is isomorphic to quequapech, thereby replacing all octagons by octagrams, resp. all ops by stops and all gircoes by quitcoes. – The 2-coloring thereof furthermore is isomorphic to gaquapech, when replacing just one half each.

The facial subset, obtained when neglecting the octagons, by itself describes the Wythoffian infinite skew polyhedron x4o6x|8, a modwrap of the hyperbolical tiling x4o6x.


Incidence matrix according to Dynkin symbol

x4x3x4x   (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
--------+-----+-----------------+----------------------+----------
x4x . . |   8 |   4   4   0   0 | 6N   *   *  *   *  * | 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 . x |   4 |   0   2   0   2 |  *   *   *  * 12N  * | 0  1  0 1
. . x4x |   8 |   0   0   4   4 |  *   *   *  *   * 6N | 0  0  1 1
--------+-----+-----------------+----------------------+----------
x4x3x .   48 |  24  24  24   0 |  6  12   0  8   0  0 | N  *  * *
x4x . x   16 |   8   8   0   8 |  2   0   4  0   4  0 | * 3N  * *
x . x4x   16 |   8   0   8   8 |  0   4   4  0   0  2 | *  * 3N *
. x3x4x   48 |   0  24  24  24 |  0   0   0  8  12  6 | *  *  * N
or
. . . .    | 24N |   2   2 |  2   2  1  1 | 2  2
-----------+-----+---------+--------------+-----
x . . .  & |   2 | 24N   * |  1   1  1  0 | 1  2
. x . .  & |   2 |   * 24N |  1   1  0  1 | 2  1
-----------+-----+---------+--------------+-----
x4x . .  & |   8 |   4   4 | 6N   *  *  * | 1  1
x . x .  & |   4 |   2   2 |  * 12N  *  * | 1  1
x . . x    |   4 |   4   0 |  *   * 6N  * | 0  2
. x3x .    |   6 |   0   6 |  *   *  * 4N | 2  0
-----------+-----+---------+--------------+-----
x4x3x .  &   48 |  24  48 |  6  12  0  8 | N  *
x4x . x  &   16 |  16   8 |  2   4  4  0 | * 3N

snubbed forms: s4x3x4x, s4s3s4s

:xxwwxx:4:xuxxux:4:wxxxxw:&##x   (N → ∞)   → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/sqrt(2) = 0.707107
                                              height(3,4) = height(6,1') = 1

 o..... 4 o..... 4 o.....      | 8N  *  *  *  *  * |  1  1  1  0  0  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  0  0 0  1  1  1 | 1  0 0 1  1 1
 .o.... 4 .o.... 4 .o....      |  * 8N  *  *  *  * |  0  0  1  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0 | 0  1  1  1  1  1 0  0  0 0  0  0  0  0 0  0  0  1 | 1  1 0 0  1 1
 ..o... 4 ..o... 4 ..o...      |  *  * 8N  *  *  * |  0  0  0  0  0  1  1  1  1  0  0  0  0  0  0  0  0  0 | 0  0  1  0  1  1 1  1  1 0  0  0  0  0 0  0  0  0 | 1  1 1 0  0 1
 ...o.. 4 ...o.. 4 ...o..      |  *  *  * 8N  *  * |  0  0  0  0  0  0  0  0  1  1  1  1  0  0  0  0  0  0 | 0  0  0  0  1  0 0  1  1 1  1  1  0  0 0  0  0  0 | 1  1 1 0  0 1
 ....o. 4 ....o. 4 ....o.      |  *  *  *  * 8N  * |  0  0  0  0  0  0  0  0  0  0  0  1  1  1  1  0  0  0 | 0  0  0  0  1  0 0  0  0 0  1  1  1  1 0  0  0  1 | 1  1 0 0  1 1
 .....o 4 .....o 4 .....o      |  *  *  *  *  * 8N |  0  0  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 0  1  0  0  1 1  1  1  1 | 1  0 0 1  1 1
-------------------------------+-------------------+-------------------------------------------------------+---------------------------------------------------+--------------
 x.....   ......   ......      |  2  0  0  0  0  0 | 4N  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  1  0  0  0  0 0  0  0 0  0  0  0  0 0  1  0  0 | 1  0 0 1  1 0
 ......   x.....   ......      |  2  0  0  0  0  0 |  * 4N  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  1  0  0  0 0  0  0 0  0  0  0  0 0  0  1  0 | 1  0 0 1  0 1
 oo.... 4 oo.... 4 oo.... &#x  |  1  1  0  0  0  0 |  *  * 8N  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1  1  0  0  0 0  0  0 0  0  0  0  0 0  0  0  1 | 1  0 0 0  1 1
 .x....   ......   ......      |  0  2  0  0  0  0 |  *  *  * 4N  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1  0  1  1  0 0  0  0 0  0  0  0  0 0  0  0  0 | 1  1 0 0  1 0
 ......   ......   .x....      |  0  2  0  0  0  0 |  *  *  *  * 4N  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  0  0  1  0  1 0  0  0 0  0  0  0  0 0  0  0  1 | 0  1 0 0  1 1
 .oo... 4 .oo... 4 .oo... &#x  |  0  1  1  0  0  0 |  *  *  *  *  * 8N  *  *  *  *  *  *  *  *  *  *  *  * | 0  0  1  0  1  1 0  0  0 0  0  0  0  0 0  0  0  0 | 1  1 0 0  0 1
 ......   ..x...   ......      |  0  0  2  0  0  0 |  *  *  *  *  *  * 4N  *  *  *  *  *  *  *  *  *  *  * | 0  0  1  0  0  0 1  1  0 0  0  0  0  0 0  0  0  0 | 1  0 1 0  0 1
 ......   ......   ..x...      |  0  0  2  0  0  0 |  *  *  *  *  *  *  * 4N  *  *  *  *  *  *  *  *  *  * | 0  0  0  0  0  1 1  0  1 0  0  0  0  0 0  0  0  0 | 0  1 1 0  0 1
 ..oo.. 4 ..oo.. 4 ..oo.. &#x  |  0  0  1  1  0  0 |  *  *  *  *  *  *  *  * 8N  *  *  *  *  *  *  *  *  * | 0  0  0  0  1  0 0  1  1 0  0  0  0  0 0  0  0  0 | 1  1 1 0  0 0
 ......   ...x..   ......      |  0  0  0  2  0  0 |  *  *  *  *  *  *  *  *  * 4N  *  *  *  *  *  *  *  * | 0  0  0  0  0  0 0  1  0 1  1  0  0  0 0  0  0  0 | 1  0 1 0  0 1
 ......   ......   ...x..      |  0  0  0  2  0  0 |  *  *  *  *  *  *  *  *  *  * 4N  *  *  *  *  *  *  * | 0  0  0  0  0  0 0  0  1 1  0  1  0  0 0  0  0  0 | 0  1 1 0  0 1
 ...oo. 4 ...oo. 4 ...oo. &#x  |  0  0  0  1  1  0 |  *  *  *  *  *  *  *  *  *  *  * 8N  *  *  *  *  *  * | 0  0  0  0  1  0 0  0  0 0  1  1  0  0 0  0  0  0 | 1  1 0 0  0 1
 ....x.   ......   ......      |  0  0  0  0  2  0 |  *  *  *  *  *  *  *  *  *  *  *  * 4N  *  *  *  *  * | 0  0  0  0  1  0 0  0  0 0  0  0  1  1 0  0  0  0 | 1  1 0 0  1 0
 ......   ......   ....x.      |  0  0  0  0  2  0 |  *  *  *  *  *  *  *  *  *  *  *  *  * 4N  *  *  *  * | 0  0  0  0  0  0 0  0  0 0  0  1  1  0 0  0  0  1 | 0  1 0 0  1 1
 ....oo 4 ....oo 4 ....oo &#x  |  0  0  0  0  1  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 8N  *  *  * | 0  0  0  0  0  0 0  0  0 0  1  0  0  1 0  0  0  1 | 1  0 0 0  1 1
 .....x   ......   ......      |  0  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 4N  *  * | 0  0  0  0  0  0 0  0  0 0  0  0  0  1 1  1  0  0 | 1  0 0 1  1 0
 ......   .....x   ......      |  0  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 4N  * | 0  0  0  0  0  0 0  0  0 0  1  0  0  0 1  0  1  0 | 1  0 0 1  0 1
:o....o:4:o....o:4:o....o:&#x  |  1  0  0  0  0  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 8N | 0  0  0  0  0  0 0  0  0 0  0  0  0  0 0  1  1  1 | 0  0 0 1  1 1
-------------------------------+-------------------+-------------------------------------------------------+---------------------------------------------------+--------------
 x..... 4 x.....   ......      |  8  0  0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | N  *  *  *  *  * *  *  * *  *  *  *  * *  *  *  * | 1  0 0 1  0 0
 xx....   ......   ...... &#x  |  2  2  0  0  0  0 |  1  0  2  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | * 4N  *  *  *  * *  *  * *  *  *  *  * *  *  *  * | 1  0 0 0  1 0
 ......   xux...   ...... &#xt |  2  2  2  0  0  0 |  0  1  2  0  0  2  1  0  0  0  0  0  0  0  0  0  0  0 | *  * 4N  *  *  * *  *  * *  *  *  *  * *  *  *  * | 1  0 0 0  0 1
 .x....   ......   .x....      |  0  4  0  0  0  0 |  0  0  0  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0 | *  *  * 2N  *  * *  *  * *  *  *  *  * *  *  *  * | 0  1 0 0  1 0
 .xwwx.   ......   ...... &#xt |  0  2  2  2  2  0 |  0  0  0  1  0  2  0  0  2  0  0  2  1  0  0  0  0  0 | *  *  *  * 4N  * *  *  * *  *  *  *  * *  *  *  * | 1  1 0 0  0 0
 ......   ......   .xx... &#x  |  0  2  2  0  0  0 |  0  0  0  0  1  2  0  1  0  0  0  0  0  0  0  0  0  0 | *  *  *  *  * 4N *  *  * *  *  *  *  * *  *  *  * | 0  1 0 0  0 1
 ......   ..x... 4 ..x...      |  0  0  8  0  0  0 |  0  0  0  0  0  0  4  4  0  0  0  0  0  0  0  0  0  0 | *  *  *  *  *  * N  *  * *  *  *  *  * *  *  *  * | 0  0 1 0  0 1
 ......   ..xx..   ...... &#x  |  0  0  2  2  0  0 |  0  0  0  0  0  0  1  0  2  1  0  0  0  0  0  0  0  0 | *  *  *  *  *  * * 4N  * *  *  *  *  * *  *  *  * | 1  0 1 0  0 0
 ......   ......   ..xx.. &#x  |  0  0  2  2  0  0 |  0  0  0  0  0  0  0  1  2  0  1  0  0  0  0  0  0  0 | *  *  *  *  *  * *  * 4N *  *  *  *  * *  *  *  * | 0  1 1 0  0 0
 ......   ...x.. 4 ...x..      |  0  0  0  8  0  0 |  0  0  0  0  0  0  0  0  0  4  4  0  0  0  0  0  0  0 | *  *  *  *  *  * *  *  * N  *  *  *  * *  *  *  * | 0  0 1 0  0 1
 ......   ...xux   ...... &#xt |  0  0  0  2  2  2 |  0  0  0  0  0  0  0  0  0  1  0  2  0  0  2  0  1  0 | *  *  *  *  *  * *  *  * * 4N  *  *  * *  *  *  * | 1  0 0 0  0 1
 ......   ......   ...xx. &#x  |  0  0  0  2  2  0 |  0  0  0  0  0  0  0  0  0  0  1  2  0  1  0  0  0  0 | *  *  *  *  *  * *  *  * *  * 4N  *  * *  *  *  * | 0  1 0 0  0 1
 ....x.   ......   ....x.      |  0  0  0  0  4  0 |  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  0  0  0 | *  *  *  *  *  * *  *  * *  *  * 2N  * *  *  *  * | 0  1 0 0  1 0
 ....xx   ......   ...... &#x  |  0  0  0  0  2  2 |  0  0  0  0  0  0  0  0  0  0  0  0  1  0  2  1  0  0 | *  *  *  *  *  * *  *  * *  *  *  * 4N *  *  *  * | 1  0 0 0  1 0
 .....x 4 .....x   ......      |  0  0  0  0  0  8 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  4  4  0 | *  *  *  *  *  * *  *  * *  *  *  *  * N  *  *  * | 1  0 0 1  0 0
:x....x:  ......   ...... &#x  |  2  0  0  0  0  2 |  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  2 | *  *  *  *  *  * *  *  * *  *  *  *  * * 4N  *  * | 0  0 0 1  1 0
 ......  :x....x:  ...... &#x  |  2  0  0  0  0  2 |  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  2 | *  *  *  *  *  * *  *  * *  *  *  *  * *  * 4N  * | 0  0 0 1  0 1
 ......   ......  :wx..xw:&#xt |  2  2  0  0  2  2 |  0  0  2  0  1  0  0  0  0  0  0  0  0  1  2  0  0  2 | *  *  *  *  *  * *  *  * *  *  *  *  * *  *  * 4N | 0  0 0 0  1 1
-------------------------------+-------------------+-------------------------------------------------------+---------------------------------------------------+--------------
 xxwwxx 4 xuxxux   ...... &#xt   8  8  8  8  8  8 |  4  4  8  4  0  8  4  0  8  4  0  8  4  0  8  4  4  0 | 1  4  4  0  4  0 0  4  0 0  4  0  0  4 1  0  0  0 | N  * * *  * *
 .xwwx.   ......   .xxxx. &#xt   0  4  4  4  4  0 |  0  0  0  2  2  4  0  2  4  0  2  4  2  2  0  0  0  0 | 0  0  0  1  2  2 0  0  2 0  0  2  1  0 0  0  0  0 | * 2N * *  * *
 ......   ..xx.. 4 ..xx.. &#x    0  0  8  8  0  0 |  0  0  0  0  0  0  4  4  8  4  4  0  0  0  0  0  0  0 | 0  0  0  0  0  0 1  4  4 1  0  0  0  0 0  0  0  0 | *  * N *  * *
:x....x:4:x....x:  ...... &#x    8  0  0  0  0  8 |  4  4  0  0  0  0  0  0  0  0  0  0  0  0  0  4  4  8 | 1  0  0  0  0  0 0  0  0 0  0  0  0  0 1  4  4  0 | *  * * N  * *
:xx..xx:  ......  :wx..xw:&#xt   4  4  0  0  4  4 |  2  0  4  2  2  0  0  0  0  0  0  0  2  2  4  2  0  4 | 0  2  0  1  0  0 0  0  0 0  0  0  1  2 0  2  0  2 | *  * * * 2N *
 ......  :xuxxux:4:wxxxxw:&#xt   8  8  8  8  8  8 |  0  4  8  0  4  8  4  4  0  4  4  8  0  4  8  0  4  8 | 0  0  4  0  0  4 1  0  0 1  4  4  0  0 0  0  4  4 | *  * * *  * N

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