complex polychoron x4-4-o2-3-o2-3-o2,
γ44
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- more general:
- xp-4-o2-3-o2-3-o2
- real space embedding:
- octo
- general polytopal classes:
- complex polytopes
links
| Acronym | ... |
| Name |
Shephard's 4-generalised tesseract, complex polychoron x4-4-o2-3-o2-3-o2, γ44 |
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| Vertex figure | tet |
| Coordinates | (in, im, ik, il) for any 1≤n,m,k,l≤4 |
| Dual | x2-3-o2-3-o2-4-o4 |
| Face vector | 256, 256, 96, 16 |
| Confer |
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External links |
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The (complex) faces are x4-4-o2, the (complex) cells are x4-4-o2-3-o2, and the vertex figure here is just x2-3-o2-3-o2, i.e. nothing but the real space tet.
The below various incidence representations are direct, next dimensional consequences from what was explained already at xp-4-o2 = xp xp. I.e. the according cartesian or prism product applies for complex polytopes alike.
Incidence matrix according to Dynkin symbol
x4-4-o2-3-o2-3-o2 . . . . | 256 ♦ 4 | 6 | 4 -----------------+-----+-----+----+--- x4 . . . | 4 | 256 | 3 | 3 -----------------+-----+-----+----+--- x4-4-o2 . . ♦ 16 | 8 | 96 | 2 -----------------+-----+-----+----+--- x4-4-o2-3-o2 . ♦ 64 | 48 | 12 | 16
x4 x4-4-o2-3-o2 . . . . | 256 ♦ 1 3 | 3 3 | 3 1 -----------------+-----+--------+-------+----- x4 . . . | 4 | 64 * | 3 0 | 3 0 . x4 . . | 4 | * 192 | 1 2 | 2 1 -----------------+-----+--------+-------+----- x4 x4 . . ♦ 16 | 4 4 | 48 * | 2 0 . x4-4-o2 . ♦ 16 | 0 8 | * 48 | 1 1 -----------------+-----+--------+-------+----- x4 x4-4-o2 . ♦ 64 | 16 32 | 8 4 | 12 * . x4-4-o2-3-o2 ♦ 64 | 0 48 | 0 12 | * 4
x4-4-o2 x4-4-o2 . . . . | 256 ♦ 2 2 | 1 4 1 | 2 2 -----------------+-----+---------+----------+---- x4 . . . | 4 | 128 * | 1 2 0 | 2 1 . . x4 . | 4 | * 128 | 0 2 1 | 1 2 -----------------+-----+---------+----------+---- x4-4-o2 . . ♦ 16 | 8 0 | 16 * * | 2 0 x4 . x4 . ♦ 16 | 4 4 | * 64 * | 1 1 . . x4-4-o2 ♦ 16 | 0 8 | * * 16 | 0 2 -----------------+-----+---------+----------+---- x4-4-o2 x4 . ♦ 64 | 32 16 | 4 8 0 | 8 * x4 . x4-4-o2 ♦ 64 | 16 32 | 0 8 4 | * 8
x4 x4 x4-4-o2 . . . . | 256 ♦ 1 1 2 | 1 2 2 1 | 2 1 1 -----------------+-----+-----------+-------------+------ x4 . . . | 4 | 64 * * | 1 2 0 0 | 2 1 0 . x4 . . | 4 | * 64 * | 1 0 2 0 | 2 0 1 . . x4 . | 4 | * * 128 | 0 1 1 1 | 1 1 1 -----------------+-----+-----------+-------------+------ x4 x4 . . ♦ 16 | 4 4 0 | 16 * * * | 2 0 0 x4 . x4 . ♦ 16 | 4 0 4 | * 32 * * | 1 1 0 . x4 x4 . ♦ 16 | 0 4 4 | * * 32 * | 1 0 1 . . x4-4-o2 ♦ 16 | 0 0 8 | * * * 16 | 0 1 1 -----------------+-----+-----------+-------------+------ x4 x4 x4 . ♦ 64 | 16 16 16 | 4 4 4 0 | 8 * * x4 . x4-4-o2 ♦ 64 | 16 0 32 | 0 8 0 4 | * 4 * . x4 x4-4-o2 ♦ 64 | 0 16 32 | 0 0 8 4 | * * 4
x4 x4 x4 x4 . . . . | 256 ♦ 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 -----------------+-----+-------------+-------------------+-------- x4 . . . | 4 | 64 * * * | 1 1 1 0 0 0 | 1 1 1 0 . x4 . . | 4 | * 64 * * | 1 0 0 1 1 0 | 1 1 0 1 . . x4 . | 4 | * * 64 * | 0 1 0 1 0 1 | 1 0 1 1 . . . x4 | 4 | * * * 64 | 0 0 1 0 1 1 | 0 1 1 1 -----------------+-----+-------------+-------------------+-------- x4 x4 . . ♦ 16 | 4 4 0 0 | 16 * * * * * | 1 1 0 0 x4 . x4 . ♦ 16 | 4 0 4 0 | * 16 * * * * | 1 0 1 0 x4 . . x4 ♦ 16 | 4 0 0 4 | * * 16 * * * | 0 1 1 0 . x4 x4 . ♦ 16 | 0 4 4 0 | * * * 16 * * | 1 0 0 1 . x4 . x4 ♦ 16 | 0 4 0 4 | * * * * 16 * | 0 1 0 1 . . x4 x4 ♦ 16 | 0 0 4 4 | * * * * * 16 | 0 0 1 1 -----------------+-----+-------------+-------------------+-------- x4 x4 x4 . ♦ 64 | 16 16 16 0 | 4 4 0 4 0 0 | 4 * * * x4 x4 . x4 ♦ 64 | 16 16 0 16 | 4 0 4 0 4 0 | * 4 * * x4 . x4 x4 ♦ 64 | 16 0 16 16 | 0 4 4 0 0 4 | * * 4 * . x4 x4 x4 ♦ 64 | 0 16 16 16 | 0 0 0 4 4 4 | * * * 4
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