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| Acronym | ahexah |
| Name | hyperbolic alternated hexagonal-tiling honeycomb |
| Circumradius | sqrt(-2/3) = 0.816497 i |
| Vertex figure |
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This non-compact hyperbolic tesselation uses the euclidean tiling trat in the sense of an infinite horohedron as one type of cells.
Incidence matrix according to Dynkin symbol
o3o3x3o3*b (N,M → ∞) . . . . | NM ♦ 12 | 12 6 | 4 4 -----------+----+-----+---------+------ . . x . | 2 | 6NM | 2 1 | 1 2 -----------+----+-----+---------+------ . o3x . | 3 | 3 | 4NM * | 1 1 . . x3o | 3 | 3 | * 2NM | 0 2 -----------+----+-----+---------+------ o3o3x . ♦ 4 | 6 | 4 0 | NM * . o3x3o3*b ♦ M | 3M | M M | * 4N
o3o3o6s (N,M → ∞)
demi( . . . . ) | NM ♦ 12 | 6 12 | 4 4
----------------+----+-----+---------+------
sefa( . . o6s ) | 2 | 6NM | 1 2 | 2 1
----------------+----+-----+---------+------
. . o6s | 3 | 3 | 2NM * | 2 0
sefa( . o3o6s ) | 3 | 3 | * 4NM | 1 1
----------------+----+-----+---------+------
. o3o6s ♦ M | 3M | M M | 4N *
sefa( o3o3o6s ) ♦ 4 | 6 | 0 4 | * NM
starting figure: o3o3o6x
s3s6o3o (N,M,K → ∞)
demi( . . . . ) | NMK ♦ 6 6 | 3 3 9 3 | 3 1 4
----------------+-----+-----------+------------------+----------
sefa( s3s . . ) | 2 | 3NMK * | 1 0 2 0 | 2 0 1
sefa( . s6o . ) | 2 | * 3NMK | 0 1 1 1 | 1 1 1
----------------+-----+-----------+------------------+----------
s3s . . | 3 | 3 0 | NMK * * * | 2 0 0
. s6o . | 3 | 0 3 | * NMK * * | 1 1 0
sefa( s3s6o . ) | 3 | 2 1 | * * 3NMK * | 1 0 1
sefa( . s6o3o ) | 3 | 0 3 | * * * NMK | 0 1 1
----------------+-----+-----------+------------------+----------
s3s6o . ♦ 3M | 6M 3M | 2M M 3M 0 | NK * *
. s6o3o ♦ K | 0 3K | 0 K 0 K | * NM *
sefa( s3s6o3o ) ♦ 4 | 3 3 | 0 0 3 1 | * * NMK
starting figure: x3x6o3o
o6s3s6o (N,M,K → ∞)
demi( . . . . ) | 3NMK ♦ 2 8 2 | 1 4 1 6 6 | 2 2 4
----------------+------+-----------------+------------------------+-------------
sefa( o6s . . ) | 2 | 3NMK * * | 1 0 0 2 0 | 2 0 1
sefa( . s3s . ) | 2 | * 12NMK * | 0 1 0 1 1 | 1 1 1
sefa( . . s6o ) | 2 | * * 3NMK | 0 0 1 0 2 | 0 2 1
----------------+------+-----------------+------------------------+-------------
o6s . . | 3 | 3 0 0 | NMK * * * * | 2 0 0
. s3s . | 3 | 0 3 0 | * 4NMK * * * | 1 1 0
. . s6o | 3 | 0 0 3 | * * NMK * * | 0 2 0
sefa( o6s3s . ) | 3 | 1 2 0 | * * * 6NMK * | 1 0 1
sefa( . s3s6o ) | 3 | 0 2 1 | * * * * 6NMK | 0 1 1
----------------+------+-----------------+------------------------+-------------
o6s3s . ♦ 3M | 3M 6M 0 | M 2M 0 3M 0 | 2NK * *
. s3s6o ♦ 3K | 0 6K 3K | 0 2K K 0 3K | * 2NM *
sefa( o6s3s6o ) ♦ 4 | 1 4 1 | 0 0 0 2 2 | * * 3NMK
starting figure: o6x3x6o
o6s3s3s3*b (N,M,K,L → ∞)
demi( . . . . ) | 3NMKL ♦ 2 4 4 2 | 1 2 2 1 3 3 6 | 1 1 2 4
-------------------+-------+-------------------------+-----------------------------------------+-------------------
sefa( o6s . . ) | 2 | 3NMKL * * * | 1 0 0 0 1 1 0 | 1 1 0 1
sefa( . s3s . ) | 2 | * 6NMKL * * | 0 1 0 0 1 0 1 | 1 0 1 1
sefa( . s . s3*b ) | 2 | * * 6NMKL * | 0 0 1 0 0 1 1 | 0 1 1 1
sefa( . . s3s ) | 2 | * * * 3NMKL | 0 0 0 1 0 0 2 | 0 0 2 1
-------------------+-------+-------------------------+-----------------------------------------+-------------------
o6s . . | 3 | 3 0 0 0 | NMKL * * * * * * | 1 1 0 0
. s3s . | 3 | 0 3 0 0 | * 2NMKL * * * * * | 1 0 1 0
. s . s3*b | 3 | 0 0 3 0 | * * 2NMKL * * * * | 0 1 1 0
. . s3s | 3 | 0 0 0 3 | * * * NMKL * * * | 0 0 2 0
sefa( o6s3s . ) | 3 | 1 2 0 0 | * * * * 3NMKL * * | 1 0 0 1
sefa( o6s . s3*b ) | 3 | 1 0 2 0 | * * * * * 3NMKL * | 0 1 0 1
sefa( . s3s3s3*b ) | 3 | 0 1 1 1 | * * * * * * 6NMKL | 0 0 1 1
-------------------+-------+-------------------------+-----------------------------------------+-------------------
o6s3s . ♦ 3M | 3M 6M 0 0 | M 2M 0 0 3M 0 0 | NKL * * *
o6s . s3*b ♦ 3K | 3K 0 6K 0 | K 0 2K 0 0 3K 0 | * NML * *
. s3s3s3*b ♦ 3L | 0 3L 3L 3L | 0 L L L 0 0 3L | * * 2NMK *
sefa( o6s3s3s3*b ) ♦ 4 | 1 2 2 1 | 0 0 0 0 1 1 2 | * * * 3NMKL
starting figure: o6x3x3x3*b
s3s3s3s3*a3*c *b3*d (N,M,K,L,P → ∞)
demi( . . . . ) | 3NMKLP ♦ 2 2 2 2 2 2 | 1 1 1 1 1 1 3 3 3 3 | 1 1 1 1 4
----------------------------+--------+-------------------------------------------+-----------------------------------------------------------------+---------------------------
sefa( s3s . . ) | 2 | 3NMKLP * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
sefa( s . s . *a3*c ) | 2 | * 3NMKLP * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
sefa( s . . s3*a ) | 2 | * * 3NMKLP * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
sefa( . s3s . ) | 2 | * * * 3NMKLP * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
sefa( . s . s *b3*d ) | 2 | * * * * 3NMKLP * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
sefa( . . s3s ) | 2 | * * * * * 3NMKLP | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
----------------------------+--------+-------------------------------------------+-----------------------------------------------------------------+---------------------------
s3s . . | 3 | 3 0 0 0 0 0 | NMKLP * * * * * * * * * | 1 1 0 0 0
s . s . *a3*c | 3 | 0 3 0 0 0 0 | * NMKLP * * * * * * * * | 1 0 1 0 0
s . . s3*a | 3 | 0 0 3 0 0 0 | * * NMKLP * * * * * * * | 0 1 1 0 0
. s3s . | 3 | 0 0 0 3 0 0 | * * * NMKLP * * * * * * | 1 0 0 1 0
. s . s *b3*d | 3 | 0 0 0 0 3 0 | * * * * NMKLP * * * * * | 0 1 0 1 0
. . s3s | 3 | 0 0 0 0 0 3 | * * * * * NMKLP * * * * | 0 0 1 1 0
sefa( s3s3s . *a3*c ) | 3 | 1 1 0 1 0 0 | * * * * * * 3NMKLP * * * | 1 0 0 0 1
sefa( s3s . s3*a *b3*d ) | 3 | 1 0 1 0 1 0 | * * * * * * * 3NMKLP * * | 0 1 0 0 1
sefa( s . s3s3*a3*c ) | 3 | 0 1 1 0 0 1 | * * * * * * * * 3NMKLP * | 0 0 1 0 1
sefa( . s3s3s *b3*d ) | 3 | 0 0 0 1 1 1 | * * * * * * * * * 3NMKLP | 0 0 0 1 1
----------------------------+--------+-------------------------------------------+-----------------------------------------------------------------+---------------------------
s3s3s . *a3*c ♦ 3M | 3M 3M 0 3M 0 0 | M M 0 M 0 0 3M 0 0 0 | NKLP * * * *
s3s . s3*a *b3*d ♦ 3K | 3K 0 3K 0 3K 0 | K 0 K 0 K 0 0 3K 0 0 | * NMLP * * *
s . s3s3*a3*c ♦ 3L | 0 3L 3L 0 0 3L | 0 L L 0 0 L 0 0 3L 0 | * * NMKP * *
. s3s3s *b3*d ♦ 3P | 0 0 0 3P 3P 3P | 0 0 0 P P P 0 0 0 3P | * * * NMKL *
sefa( s3s3s3s3*a3*c *b3*d ) ♦ 4 | 1 1 1 1 1 1 | 0 0 0 0 0 0 1 1 1 1 | * * * * 3NMKLP
starting figure: x3x3x3x3*a3*c *b3*d
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