hyperbolic honeycomb with seed point at vertex of right-angled octahedron domain
©
©
- general polytopal classes:
- regular noble polytopes
links
| Acronym | sisquah |
| Name |
hyperbolic order 4 square-tiling honeycomb, hyperbolic honeycomb with seed point at vertex of right-angled octahedron domain |
| |
| Circumradius | 0 i |
| Dual | (selfdual) |
| Vertex figure |
|
| Confer |
|
|
External links |
|
This regular, non-compact hyperbolic tesselation uses the (q scaled) euclidean tiling squat in the sense of an infinite horohedron as vertex figure. An (unit) squat in the sense of an infinite horohedron is its single cell type too.
Incidence matrix according to Dynkin symbol
x4o4o4o (N,M,K → ∞) . . . . | 2NK ♦ M | 2M | M --------+-----+-----+-----+---- x . . . | 2 | NMK | 4 | 4 --------+-----+-----+-----+---- x4o . . | 4 | 4 | NMK | 2 --------+-----+-----+-----+---- x4o4o . ♦ K | 2K | K | 2NM snubbed forms: x4o4o4o
x4o4o *b4o (N,M,K,L → ∞) . . . . | NKL ♦ 2M | 4M | M M -----------+-----+------+------+-------- x . . . | 2 | NMKL | 4 | 2 2 -----------+-----+------+------+-------- x4o . . | 4 | 4 | NMKL | 1 1 -----------+-----+------+------+-------- x4o4o . ♦ K | 2K | K | NML * x4o . *b4o ♦ L | 2L | L | * NMK snubbed forms: s4o4o *b4o
x4o4o4o4*a (N,M,K,L,P → ∞) . . . . | NKLP ♦ 4M | 4M 4M | M 2M M -----------+------+--------+-------------+--------------- x . . . | 2 | 2NMKLP | 2 2 | 1 2 1 -----------+------+--------+-------------+--------------- x4o . . | 4 | 4 | NMKLP * | 1 1 0 x . . o4*a | 4 | 4 | * NMKLP | 0 1 1 -----------+------+--------+-------------+--------------- x4o4o . ♦ K | 2K | K 0 | NMLP * * x4o . o4*a ♦ 2L | 4L | L L | * NMKP * x . o4o4*a ♦ P | 2P | 0 P | * * NMKL snubbed forms: s4o4o4o4*a
s4o4o4o (N,M,K,L → ∞)
demi( . . . . ) | NKL ♦ 2M | 4M | M M
----------------+-----+------+------+--------
s4o . . | 2 | NMKL | 4 | 2 2
----------------+-----+------+------+--------
sefa( s4o4o . ) | 4 | 4 | NMKL | 1 1
----------------+-----+------+------+--------
s4o4o . ♦ K | 2K | K | NML *
sefa( s4o4o4o ) ♦ L | 2L | L | * NMK
starting figure: x4o4o4o
s4o4o *b4o (N,M,K,L,P → ∞)
demi( . . . . ) | NMKLP ♦ 4M | 4M 4M | M M 2M
-------------------+-------+--------+-------------+---------------
s4o . . | 2 | 2NMKLP | 2 2 | 1 1 2
-------------------+-------+--------+-------------+---------------
sefa( s4o4o . ) | 4 | 4 | NMKLP * | 1 0 1
sefa( s4o . *b4o ) | 4 | 4 | * NMKLP | 0 1 1
-------------------+-------+--------+-------------+---------------
s4o4o . ♦ K | 2K | K 0 | NMLP * *
s4o . *b4o ♦ L | 2L | 0 L | * NMKP *
sefa( s4o4o *b4o ) ♦ 2P | 4P | P P | * * NMKL
starting figure: x4o4o *b4o
s4o4o4o4*a (N,M,K,L,P,Q → ∞)
demi( . . . . ) | NMKLPQ ♦ 4M 4M | 4M 8M 4M | M 2M M 4M
-------------------+--------+-----------------+-----------------------+-------------------------
s4o . . | 2 | 2NMKLPQ * | 2 2 0 | 1 1 0 2
s . . o4*a | 2 | * 2NMKLPQ | 0 2 2 | 0 1 1 2
-------------------+--------+-----------------+-----------------------+-------------------------
sefa( s4o4o . ) | 4 | 4 0 | NMKLPQ * * | 1 0 0 1
sefa( s4o . o4*a ) | 4 | 2 2 | * 2NMKLPQ * | 0 1 0 1
sefa( s . o4o4*a ) | 4 | 0 4 | * * NMKLPQ | 0 0 1 1
-------------------+--------+-----------------+-----------------------+-------------------------
s4o4o . ♦ K | 2K 0 | K 0 0 | NMLPQ * * *
s4o . o4*a ♦ L | L L | 0 L 0 | * 2NMKPQ * *
s . o4o4*a ♦ P | 0 2P | 0 0 P | * * NMKLQ *
sefa( s4o4o4o4*a ) ♦ 4Q | 4Q 4Q | Q 2Q Q | * * * NMKLP
starting figure: x4o4o4o4*a
x4oØo4*a4oØo4*a (N,M,K,L,P,Q → ∞) . . . . . | 2NKLPQ ♦ 4M | 2M 2M 2M 2M | M M M M ----------------+--------+---------+-----------------------------+------------------------ x . . . . | 2 | 4NMKLPQ | 1 1 1 1 | 1 1 1 1 ----------------+--------+---------+-----------------------------+------------------------ x4o . . . | 4 | 4 | NMKLPQ * * * | 1 1 0 0 x . o4*a . . | 4 | 4 | * NMKLPQ * * | 0 0 1 1 x . . *a4o . | 4 | 4 | * * NMKLPQ * | 1 0 1 0 x . . . o4*a | 4 | 4 | * * * NMKLPQ | 0 1 0 1 ----------------+--------+---------+-----------------------------+------------------------ x4o . *a4o . ♦ 2K | 4K | K 0 K 0 | NMLPQ * * * x4o . . o4*a ♦ 2L | 4L | L 0 0 L | * NMKPQ * * x . o4*a4o . ♦ 2P | 4P | 0 P P 0 | * * NMKLQ * x . o4*a . o4*a ♦ 2Q | 4Q | 0 Q 0 Q | * * * NMKLP
o4xØo4*a4xØo4*a (N,M,K,L,P,Q → ∞) . . . . . | NKLPQ ♦ 4M 4M | 4M 4M 8M | 4M M M 2M ----------------+-------+-----------------+-----------------------+------------------------- . x . . . | 2 | 2NMKLPQ * | 2 0 2 | 2 1 0 1 . . . x . | 2 | * 2NMKLPQ | 0 2 2 | 2 0 1 1 ----------------+-------+-----------------+-----------------------+------------------------- o4x . . . | 4 | 4 0 | NMKLPQ * * | 1 1 0 0 o . . *a4x . | 4 | 0 4 | * NMKLPQ * | 1 0 1 0 . x . x . | 4 | 2 2 | * * 2NMKLPQ | 1 0 0 1 ----------------+-------+-----------------+-----------------------+------------------------- o4x . *a4x . ♦ 4K | 4K 4K | K K 2K | NMLPQ * * * o4x . . o4*a ♦ L | 2L 0 | L 0 0 | * NMKPQ * * o . o4*a4x . ♦ P | 0 2P | 0 P 0 | * * NMKLQ * . xØo xØo ♦ Q | Q Q | 0 0 Q | * * * 2NMKLP
octahedral Coxeter domain with boundary pattern:
b e
g a
h c
d f
oØoØxØxØoØxØoØxØ*aØ*cØ*gØ*eØ*hØ*fØ*bØ*dØ*a (N,M,K,L,P,Q,R → ∞)
a b c d e f g h
. . . . . . . . | NKLPQR ♦ 2M 2M 2M 2M | 4M 4M 4M 4M | M M M M 4M
-------------------------------------------+--------+---------------------------------+---------------------------------+-----------------------------------
. . x . . . . . | 2 | NMKLPQR * * * | 2 2 0 0 | 1 0 1 0 2
. . . x . . . . | 2 | * NMKLPQR * * | 0 0 2 2 | 0 1 0 1 2
. . . . . x . . | 2 | * * NMKLPQR * | 2 0 2 0 | 1 1 0 0 2
. . . . . . . x | 2 | * * * NMKLPQR | 0 2 0 2 | 0 0 1 1 2
-------------------------------------------+--------+---------------------------------+---------------------------------+-----------------------------------
. . x . . x . . | 4 | 2 0 2 0 | NMKLPQR * * * | 1 0 0 0 1
. . x . . . . x | 4 | 2 0 0 2 | * NMKLPQR * * | 0 0 1 0 1
. . . x . x . . | 4 | 0 2 2 0 | * * NMKLPQR * | 0 1 0 0 1
. . . x . . . x | 4 | 0 2 0 2 | * * * NMKLPQR | 0 0 0 1 1
-------------------------------------------+--------+---------------------------------+---------------------------------+-----------------------------------
o . x . oØx . . *aØ*c ♦ K | K 0 K 0 | K 0 0 0 | NMLPQR * * * *
o . . x . xØo . *dØ*a ♦ L | 0 L L 0 | 0 0 L 0 | * NMKPQR * * *
. oØx . o . . x *eØ*h ♦ P | P 0 0 P | 0 P 0 0 | * * NMKLQR * *
. o . x . . oØx *bØ*d ♦ Q | 0 Q 0 Q | 0 0 0 Q | * * * NMKLPR *
. . xØx . x . x *hØ*f ♦ 4R | 2R 2R 2R 2R | R R R R | * * * * NMKLPQ
© 2004-2024 | top of page |