runcitruncated cubic honeycomb
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- general polytopal classes:
- partial Stott expansions
links
| Acronym | prich |
| Name |
prismatorhombated cubic honeycomb, runcitruncated cubic honeycomb |
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| Vertex figure |
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| Confer |
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External links |
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As abstract polychoron prich is isomorphic to paqrich, thereby replacing sirco by querco. – It also is isomorph to quiprich, then replacing octagons by octagrams, resp. tic by quith and op by stop. – Finally it is isomorph to quipqrich, thereby doing both changes at once.
Incidence matrix according to Dynkin symbol
x4x3o4x (N → ∞) . . . . | 24N | 1 2 2 | 2 2 1 2 1 | 1 2 1 1 --------+-----+-------------+------------------+---------- x . . . | 2 | 12N * * | 2 2 0 0 0 | 1 2 1 0 . x . . | 2 | * 24N * | 1 0 1 1 0 | 1 1 0 1 . . . x | 2 | * * 24N | 0 1 0 1 1 | 0 1 1 1 --------+-----+-------------+------------------+---------- x4x . . | 8 | 4 4 0 | 6N * * * * | 1 1 0 0 x . . x | 4 | 2 0 2 | * 12N * * * | 0 1 1 0 . x3o . | 3 | 0 3 0 | * * 8N * * | 1 0 0 1 . x . x | 4 | 0 2 2 | * * * 12N * | 0 1 0 1 . . o4x | 4 | 0 0 4 | * * * * 6N | 0 0 1 1 --------+-----+-------------+------------------+---------- x4x3o . ♦ 24 | 12 24 0 | 6 0 8 0 0 | N * * * x4x . x ♦ 16 | 8 8 8 | 2 4 0 4 0 | * 3N * * x . o4x ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 3N * . x3o4x ♦ 24 | 0 24 24 | 0 0 8 12 6 | * * * N snubbed forms: s4x3o4s, s4x3o4x, x4x3o4s
:xxxx:4:xoox:4:xwwx:&##x (N → ∞) → heights alternatingly = 1/sqrt(2) = 0.707107 resp. = 1 o... 4 o... 4 o... | 8N * * * | 1 1 1 1 0 0 0 0 0 0 0 1 | 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 | 1 1 0 1 1 1 .o.. 4 .o.. 4 .o.. | * 4N * * | 0 0 0 2 2 1 0 0 0 0 0 0 | 0 0 2 1 2 1 2 0 0 0 0 0 0 0 0 | 2 1 1 1 0 0 ..o. 4 ..o. 4 ..o. | * * 4N * | 0 0 0 0 0 1 2 2 0 0 0 0 | 0 0 0 0 2 0 2 1 2 1 0 0 0 0 0 | 2 1 1 1 0 0 ...o 4 ...o 4 ...o | * * * 8N | 0 0 0 0 0 0 0 1 1 1 1 1 | 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 | 1 1 0 1 1 1 -------------------------+-------------+-------------------------------------+------------------------------------------+-------------- x... .... .... | 2 0 0 0 | 4N * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 | 1 0 0 1 1 0 .... x... .... | 2 0 0 0 | * 4N * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 | 0 1 0 1 0 1 .... .... x... | 2 0 0 0 | * * 4N * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 | 1 1 0 0 1 1 oo.. 4 oo.. 4 oo.. &#x | 1 1 0 0 | * * * 8N * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 .x.. .... .... | 0 2 0 0 | * * * * 4N * * * * * * * | 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 .oo. 4 .oo. 4 .oo. &#x | 0 1 1 0 | * * * * * 4N * * * * * * | 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 | 2 1 1 0 0 0 ..x. .... .... | 0 0 2 0 | * * * * * * 4N * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 1 0 1 1 0 0 ..oo 4 ..oo 4 ..oo &#x | 0 0 1 1 | * * * * * * * 8N * * * * | 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 0 ...x .... .... | 0 0 0 2 | * * * * * * * * 4N * * * | 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 | 1 0 0 1 1 0 .... ...x .... | 0 0 0 2 | * * * * * * * * * 4N * * | 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 0 1 .... .... ...x | 0 0 0 2 | * * * * * * * * * * 4N * | 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 | 1 1 0 0 1 1 :o..o:4:o..o:4:o..o:&#x | 1 0 0 1 | * * * * * * * * * * * 8N | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1 -------------------------+-------------+-------------------------------------+------------------------------------------+-------------- x... .... x... | 4 0 0 0 | 2 0 2 0 0 0 0 0 0 0 0 0 | 2N * * * * * * * * * * * * * * | 1 0 0 0 1 0 .... x... 4 x... | 8 0 0 0 | 0 4 4 0 0 0 0 0 0 0 0 0 | * N * * * * * * * * * * * * * | 0 1 0 0 0 1 xx.. .... .... &#x | 2 2 0 0 | 1 0 0 2 1 0 0 0 0 0 0 0 | * * 4N * * * * * * * * * * * * | 1 0 0 1 0 0 .... xo.. .... &#x | 2 1 0 0 | 0 1 0 2 0 0 0 0 0 0 0 0 | * * * 4N * * * * * * * * * * * | 0 1 0 1 0 0 .... .... xwwx &#xt | 2 2 2 2 | 0 0 1 2 0 2 0 2 0 0 1 0 | * * * * 4N * * * * * * * * * * | 1 1 0 0 0 0 .x.. 4 .o.. .... | 0 4 0 0 | 0 0 0 0 4 0 0 0 0 0 0 0 | * * * * * N * * * * * * * * * | 0 0 1 1 0 0 .xx. .... .... &#x | 0 2 2 0 | 0 0 0 0 1 2 1 0 0 0 0 0 | * * * * * * 4N * * * * * * * * | 1 0 1 0 0 0 ..x. 4 ..o. .... | 0 0 4 0 | 0 0 0 0 0 0 4 0 0 0 0 0 | * * * * * * * N * * * * * * * | 0 0 1 1 0 0 ..xx .... .... &#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 0 0 0 | * * * * * * * * 4N * * * * * * | 1 0 0 1 0 0 .... ..ox .... &#x | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * * 4N * * * * * | 0 1 0 1 0 0 ...x .... ...x | 0 0 0 4 | 0 0 0 0 0 0 0 0 2 0 2 0 | * * * * * * * * * * 2N * * * * | 1 0 0 0 1 0 .... ...x 4 ...x | 0 0 0 8 | 0 0 0 0 0 0 0 0 0 4 4 0 | * * * * * * * * * * * N * * * | 0 1 0 0 0 1 :x..x: .... .... &#x | 2 0 0 2 | 1 0 0 0 0 0 0 0 1 0 0 2 | * * * * * * * * * * * * 4N * * | 0 0 0 1 1 0 .... :x..x: .... &#x | 2 0 0 2 | 0 1 0 0 0 0 0 0 0 1 0 2 | * * * * * * * * * * * * * 4N * | 0 0 0 1 0 1 .... .... :x..x:&#x | 2 0 0 2 | 0 0 1 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * * * * * 4N | 0 0 0 0 1 1 -------------------------+-------------+-------------------------------------+------------------------------------------+-------------- xxxx .... xwwx &#xt ♦ 4 4 4 4 | 2 0 2 4 2 4 2 4 2 0 2 0 | 1 0 2 0 2 0 2 0 2 0 1 0 0 0 0 | 2N * * * * * .... xoox 4 xwwx &#xt ♦ 8 4 4 8 | 0 4 4 8 0 4 0 8 0 4 4 0 | 0 1 0 4 4 0 0 0 0 4 0 1 0 0 0 | * N * * * * .xx. 4 .oo. .... &#x ♦ 0 4 4 0 | 0 0 0 0 4 4 4 0 0 0 0 0 | 0 0 0 0 0 1 4 1 0 0 0 0 0 0 0 | * * N * * * :xxxx:4:xoox: .... &#xt ♦ 8 4 4 8 | 4 4 0 8 4 0 4 8 4 4 0 8 | 0 0 4 4 0 1 0 1 4 4 0 0 4 4 0 | * * * N * * :x..x: .... :x..x:&#x ♦ 4 0 0 4 | 2 0 2 0 0 0 0 0 2 0 2 4 | 1 0 0 0 0 0 0 0 0 0 1 0 2 0 2 | * * * * 2N * .... :x..x:4:x..x:&#x ♦ 8 0 0 8 | 0 4 4 0 0 0 0 0 0 4 4 8 | 0 1 0 0 0 0 0 0 0 0 0 1 0 4 4 | * * * * * N
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