omnitruncated cubic honeycomb
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| Acronym | gippich (old: otch) |
| Name |
great prismated cubic honeycomb, omnitruncated cubic honeycomb |
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| Vertex figure |
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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, s4x3x4s, x4s3s4x, 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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