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- related hyperbolic polytopes:
- x3o6o3o o6x3o3o3*b o3x6o3o
- general polytopal classes:
- partial Stott expansions regular noble polytopes
links
| Acronym | hexah |
| Name | hyperbolic order 3 hexagonal-tiling honeycomb |
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| Circumradius | sqrt(-2) = 1.414214 i |
| Vertex figure |
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| Dual | thon |
| Confer |
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External links |
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This regular non-compact hyperbolic tesselation uses hexat in the sense of an infinite horohedron as its only cell type.
Incidence matrix according to Dynkin symbol
o3o3o6x (N,M → ∞) . . . . | NM ♦ 4 | 6 | 4 --------+----+-----+----+--- . . . x | 2 | 2NM | 3 | 3 --------+----+-----+----+--- . . o6x | 6 | 6 | NM | 2 --------+----+-----+----+--- . o3o6x ♦ 2M | 3M | M | 2N snubbed forms: o3o3o6s
x3x6o3o (N,M,K → ∞) . . . . | 2NMK ♦ 1 3 | 3 3 | 3 1 --------+------+----------+---------+------ x . . . | 2 | NMK * | 3 0 | 3 0 . x . . | 2 | * 3NMK | 1 2 | 2 1 --------+------+----------+---------+------ x3x . . | 6 | 3 3 | NMK * | 2 0 . x6o . | 6 | 0 6 | * NMK | 1 1 --------+------+----------+---------+------ x3x6o . ♦ 6M | 3M 6M | 2M M | NK * . x6o3o ♦ 2K | 0 3K | 0 K | * NM snubbed forms: s3s6o3o
o6x3x6o (N,M,K → ∞) . . . . | 6NMK ♦ 2 2 | 1 4 1 | 2 2 --------+------+-----------+--------------+-------- . x . . | 2 | 6NMK * | 1 2 0 | 2 1 . . x . | 2 | * 6NMK | 0 2 1 | 1 2 --------+------+-----------+--------------+-------- o6x . . | 6 | 6 0 | NMK * * | 2 0 . x3x . | 6 | 3 3 | * 4NMK * | 1 1 . . x6o | 6 | 0 6 | * * NMK | 0 2 --------+------+-----------+--------------+-------- o6x3x . ♦ 6M | 6M 3M | M 2M 0 | 2NK * . x3x6o ♦ 6K | 3K 6K | 0 2K K | * 2NM snubbed forms: o6s3s6o
o6x3x3x3*b (N,M,K,L → ∞) . . . . | 6NMKL ♦ 2 1 1 | 1 2 2 1 | 1 1 2 -----------+-------+-------------------+-----------------------+------------- . x . . | 2 | 6NMKL * * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 3NMKL * | 0 2 0 1 | 1 0 2 . . . x | 2 | * * 3NMKL | 0 0 2 1 | 0 1 2 -----------+-------+-------------------+-----------------------+------------- o6x . . | 6 | 6 0 0 | NMKL * * * | 1 1 0 . x3x . | 6 | 3 3 0 | * 2NMKL * * | 1 0 1 . x . x3*b | 6 | 3 0 3 | * * 2NMKL * | 0 1 1 . . x3x | 6 | 0 3 3 | * * * NMKL | 0 0 2 -----------+-------+-------------------+-----------------------+------------- o6x3x . ♦ 6M | 6M 3M 0 | M 2M 0 0 | NKL * * o6x . x3*b ♦ 6K | 6K 0 3K | K 0 2K 0 | * NML * . x3x3x3*b ♦ 6L | 3L 3L 3L | 0 L L L | * * 2NMK snubbed forms: o6s3s3s3*b
x3x3x3x3*a3*c *b3*d (N,M,K,L,P → ∞) . . . . | 6NMKLP ♦ 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 --------------------+--------+-----------------------------+-------------------------------------+-------------------- x . . . | 2 | 3NMKLP * * * | 1 1 1 0 0 0 | 1 1 1 0 . x . . | 2 | * 3NMKLP * * | 1 0 0 1 1 0 | 1 1 0 1 . . x . | 2 | * * 3NMKLP * | 0 1 0 1 0 1 | 1 0 1 1 . . . x | 2 | * * * 3NMKLP | 0 0 1 0 1 1 | 0 1 1 1 --------------------+--------+-----------------------------+-------------------------------------+-------------------- x3x . . | 6 | 3 3 0 0 | NMKLP * * * * * | 1 1 0 0 x . x . *a3*c | 6 | 3 0 3 0 | * NMKLP * * * * | 1 0 1 0 x . . x3*a | 6 | 3 0 0 3 | * * NMKLP * * * | 0 1 1 0 . x3x . | 6 | 0 3 3 0 | * * * NMKLP * * | 1 0 0 1 . x . x *b3*d | 6 | 0 3 0 3 | * * * * NMKLP * | 0 1 0 1 . . x3x | 6 | 0 0 3 3 | * * * * * NMKLP | 0 0 1 1 --------------------+--------+-----------------------------+-------------------------------------+-------------------- x3x3x . *a3*c ♦ 6M | 3M 3M 3M 0 | M M 0 M 0 0 | NKLP * * * x3x . x3*a *b3*d ♦ 6K | 3K 3K 0 3K | K 0 K 0 K 0 | * NMLP * * x . x3x3*a3*c ♦ 6L | 3L 0 3L 3L | 0 L L 0 0 L | * * NMKP * . x3x3x *b3*d ♦ 6P | 0 3P 3P 3P | 0 0 0 P P P | * * * NMKL snubbed forms: s3s3s3s3*a3*c *b3*d
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