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| 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 right Herschel graph, where the mentioned pole vertices would be the left and right blue dots.)
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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