Acronym | srotehat |
Name | hyperbolic (small) rhombisquarehexagonal tiling |
© | |
Circumradius | sqrt[-3-2 sqrt(6)]/2 = 1.405256 i |
Vertex figure | [43,6] |
External links |
There exists a regular modwrap of this tiling, obtained by identifying every 8th vertex on each hole. Then it allows a representation as infinite skew polyhedron, which happens to be a facial subset of the omnitruncated cubical honeycomb. (The rightmost pictures hint on its relation to x4o6o|4 and x6o4o|4 resp.)
Incidence matrix according to Dynkin symbol
x4o6x (N → ∞) . . . | 12N | 2 2 | 1 2 1 ------+-----+---------+--------- x . . | 2 | 12N * | 1 1 0 . . x | 2 | * 12N | 0 1 1 ------+-----+---------+--------- x4o . | 4 | 4 0 | 3N * * x . x | 4 | 2 2 | * 6N * . o6x | 6 | 0 6 | * * 2N snubbed forms: s4o6x, x4o6s, s4o6s'
s4s6x (N → ∞) demi( . . . ) | 12N | 1 2 1 | 1 1 2 --------------+-----+-----------+--------- demi( . . x ) | 2 | 6N * * | 0 1 1 sefa( s4s . ) | 2 | * 12N * | 1 0 1 sefa( . s6x ) | 2 | * * 6N | 0 1 1 --------------+-----+-----------+--------- s4s . | 4 | 0 4 0 | 3N * * . s6x | 6 | 3 0 3 | * 2N * sefa( s4s6x ) | 4 | 1 2 1 | * * 6N starting figure: x4x6x
x4s6s (N → ∞) demi( . . . ) | 12N | 1 1 2 | 1 1 2 --------------+-----+-----------+--------- demi( x . . ) | 2 | 6N * * | 1 0 1 sefa( x4s . ) | 2 | * 6N * | 1 0 1 sefa( . s6s ) | 2 | * * 12N | 0 1 1 --------------+-----+-----------+--------- x4s . | 4 | 2 2 0 | 3N * * . s6s | 6 | 0 0 6 | * 2N * sefa( x4s6s ) | 4 | 1 1 2 | * * 6N starting figure: x4x6x
x4s6x (N → ∞) demi( . . . ) | 12N | 1 1 1 1 | 1 1 1 1 --------------+-----+-------------+------------ demi( x . . ) | 2 | 6N * * * | 1 1 0 0 demi( . . x ) | 2 | * 6N * * | 1 0 1 0 sefa( x4s . ) | 2 | * * 6N * | 0 1 0 1 sefa( . s4x ) | 2 | * * * 6N | 0 0 1 1 --------------+-----+-------------+------------ demi( x . x ) | 4 | 2 2 0 0 | 3N * * * x4s . | 4 | 2 0 2 0 | * 3N * * . s6x | 6 | 0 3 0 3 | * * 2N * sefa( x4s6x ) | 4 | 0 0 2 2 | * * * 3N starting figure: x4x6x
xØx3xØx (N → ∞) . . . . | 12N | 1 1 1 1 | 1 1 1 1 --------+-----+-------------+------------ x . . . | 2 | 6N * * * | 1 1 0 0 . x . . | 2 | * 6N * * | 0 0 1 1 . . x . | 2 | * * 6N * | 1 0 1 0 . . . x | 2 | * * * 6N | 0 1 0 1 --------+-----+-------------+------------ x . x . | 4 | 2 0 2 0 | 3N * * * x . . x | 4 | 2 0 0 2 | * 3N * * . x3x . | 6 | 0 3 3 0 | * * 2N * . x . x | 4 | 0 2 0 2 | * * * 3N
© 2004-2024 | top of page |