| Acronym | ... |
| Name | hyperbolic honeycomb with seed point at face of right-angled octahedron domain |
This non-compact hyperbolic tesselation uses the euclidean tiling squat in the sense of an infinite horohedron as its single cell type.
The vertex figure here is kind a threefold axial version of (the axially forefold) rad with three rhombs connected to the poles each and further three rhombs around its equator. (Its edge skeleton would be a representation of the Herschel graph.)
Incidence matrix according to Dynkin symbol
octahedral Coxeter domain with boundary pattern:
b e
g a
h c
d f
oØxØxØxØxØxØxØxØ*aØ*cØ*gØ*eØ*hØ*fØ*bØ*dØ*a (N,M,K,L,P,Q,R → ∞)
a b c d e f g h
. . . . . . . . | 2NMKLPQR | 2 2 2 1 1 1 2 | 2 2 2 2 2 2 2 2 2 | 1 1 1 2 2 2
-------------------------------------------+----------+-------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------
. x . . . . . . | 2 | 2NMKLPQR * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 0 0 1 1 0
. . x . . . . . | 2 | * 2NMKLPQR * * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 0 1 0 1
. . . x . . . . | 2 | * * 2NMKLPQR * * * * | 0 0 0 0 0 0 1 1 1 | 0 0 1 0 1 1
. . . . x . . . | 2 | * * * NMKLPQR * * * | 2 0 0 2 0 0 0 0 0 | 1 1 0 2 0 0
. . . . . x . . | 2 | * * * * NMKLPQR * * | 0 0 0 0 2 0 2 0 0 | 0 1 1 0 0 2
. . . . . . x . | 2 | * * * * * NMKLPQR * | 0 2 0 0 0 0 0 2 0 | 1 0 1 0 2 0
. . . . . . . x | 2 | * * * * * * 2NMKLPQR | 0 0 1 0 0 1 0 0 1 | 0 0 0 1 1 1
-------------------------------------------+----------+-------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------
. x . . x . . . | 4 | 2 0 0 2 0 0 0 | NMKLPQR * * * * * * * * | 1 0 0 1 0 0
. x . . . . x . | 4 | 2 0 0 0 0 2 0 | * NMKLPQR * * * * * * * | 1 0 0 0 1 0
. x . . . . . x | 4 | 2 0 0 0 0 0 2 | * * NMKLPQR * * * * * * | 0 0 0 1 1 0
. . x . x . . . | 4 | 0 2 0 2 0 0 0 | * * * NMKLPQR * * * * * | 0 1 0 1 0 0
. . x . . x . . | 4 | 0 2 0 0 2 0 0 | * * * * NMKLPQR * * * * | 0 1 0 0 0 1
. . x . . . . x | 4 | 0 2 0 0 0 0 2 | * * * * * NMKLPQR * * * | 0 0 0 1 0 1
. . . x . x . . | 4 | 0 0 2 0 2 0 0 | * * * * * * NMKLPQR * * | 0 0 1 0 0 1
. . . x . . x . | 4 | 0 0 2 0 0 2 0 | * * * * * * * NMKLPQR * | 0 0 1 0 1 0
. . . x . . . x | 4 | 0 0 2 0 0 0 2 | * * * * * * * * NMKLPQR | 0 0 0 0 1 1
-------------------------------------------+----------+-------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------
oØx . . x . x . *gØ*e ♦ 2M | 2M 0 0 M 0 M 0 | M M 0 0 0 0 0 0 0 | NKLPQR * * * * *
o . x . xØx . . *aØ*c ♦ 2K | 0 2K 0 K K 0 0 | 0 0 0 K K 0 0 0 0 | * NMLPQR * * * *
o . . x . xØx . *dØ*a ♦ 2L | 0 0 2L 0 L L 0 | 0 0 0 0 0 0 L L 0 | * * NMKPQR * * *
. xØx . x . . x *eØ*h ♦ 4P | 2P 2P 0 2P 0 0 2P | P 0 P P 0 P 0 0 0 | * * * NMKLQR * *
. x . x . . xØx *bØ*d ♦ 4Q | 2Q 0 2Q 0 0 2Q 2Q | 0 Q Q 0 0 0 0 Q Q | * * * * NMKLPR *
. . xØx . x . x *hØ*f ♦ 4R | 0 2R 2R 0 2R 0 2R | 0 0 0 0 R R R 0 R | * * * * * NMKLPQ
or 2NMK | 2 6 3 | 6 12 | 6 3 -----+----------------+-----------+-------- 2 | 2NMK * * | 3 0 | 3 0 2 | * 6NMK * | 1 2 | 2 1 2 | * * 3NMK | 0 4 | 2 2 -----+----------------+-----------+-------- 4 | 2 2 0 | 3NMK * | 2 0 4 | 0 2 2 | * 6NMK | 1 1 -----+----------------+-----------+-------- ♦ 2M | M 2M M | M M | 6NK * ♦ K | 0 K K | 0 K | * 6NM
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