Acronym | ... |
Name | lamina-truncate of hyperbolic o8o4x *b3x tesselation |
Circumradius | sqrt[1-sqrt(2)]/2 = 0.321797 i |
Vertex figure | oxqxo8ooooo&#qt |
Confer |
|
As the order 8 square tiling (osquat) within o8o4x *b3x were hemi-choral (have same curvature resp. intersect the sphere of infinity orthogonally) those could be replaced by mirror images of the remainder each. This alone then results in o8o4x *b3xØx3*b. Further the order 8 triangle tiling (otrat) there allows for an attaching layer of trips, as taken from x x3o8o. The magic then is, that the bollo-surface through their center points again happens to be hemi-choral, thus there too a second type of mirror can be placed. Accordingly we thus obtain this still uniform and again compact lamina-truncate, built from sircoes and trips only. (In fact, if only the latter mirroring would take place, and not the former, then one would obtain o8o3x *b4xØx instead.)
Note that this double blending is correlated to the according blends of the vertex figure at its tropal x8o layers and at its equatorial q8o layer respectively. Accordingly we do need here two different non-joiners Ø' and Ø". Each geometrical blend reflects itself in a blend of the former's Dynkin diagram along the being blended out subsymbol. The not therein contained node pairs thereby are then to be linked by the according non-joiner.
lamina-truncate( o8o4x *b3x ) (N → ∞) 3N ♦ 2 16 8 | 16 16 16 8 | 16 16 ---+------------+----------------+------ 2 | 3N * * | 8 0 0 0 | 8 0 2 | * 24N * | 1 2 1 0 | 2 2 2 | * * 12N | 0 0 2 2 | 0 4 ---+------------+----------------+------ 4 | 2 2 0 | 12N * * * | 2 0 3 | 0 3 0 | * 16N * * | 1 1 4 | 0 2 2 | * * 12N * | 0 2 4 | 0 0 4 | * * * 6N | 0 2 ---+------------+----------------+------ 6 | 3 6 0 | 3 2 0 0 | 8N * trip 24 | 0 24 24 | 0 8 12 6 | * 2N sirco
o8o3xØ'x3*b4xØ"xØ'xØ"*e (N → ∞) . . . . . . . | 6N | 8 8 8 1 1 | 8 8 8 8 8 8 8 | 8 8 8 8 ------------------------+----+-------------------+-----------------------------+------------ . . x . . . . | 2 | 24N * * * * | 2 0 0 1 1 0 0 | 2 2 0 0 . . . x . . . | 2 | * 24N * * * | 0 2 0 0 0 1 1 | 0 0 2 2 . . . . x . . | 2 | * * 24N * * | 0 0 2 1 0 1 0 | 2 0 2 0 . . . . . x . | 2 | * * * 3N * | 0 0 0 0 8 0 0 | 0 8 0 0 . . . . . . x | 2 | * * * * 3N | 0 0 0 0 0 0 8 | 0 0 0 8 ------------------------+----+-------------------+-----------------------------+------------ . o3x . . . . | 3 | 3 0 0 0 0 | 16N * * * * * * | 1 1 0 0 . o . x3*b . . . | 3 | 0 3 0 0 0 | * 16N * * * * * | 0 0 1 1 . o . . *b4x . . | 4 | 0 0 4 0 0 | * * 12N * * * * | 1 0 1 0 . . x . x . . | 4 | 2 0 2 0 0 | * * * 12N * * * | 2 0 0 0 . . x . . x . | 4 | 2 0 0 2 0 | * * * * 12N * * | 0 2 0 0 . . . x x . . | 4 | 0 2 2 0 0 | * * * * * 12N * | 0 0 2 0 . . . x . . x | 4 | 0 2 0 0 2 | * * * * * * 12N | 0 0 0 2 ------------------------+----+-------------------+-----------------------------+------------ . o3x . *b4x . . | 24 | 24 0 24 0 0 | 8 0 6 12 0 0 0 | 2N * * * sirco . o3x . . x . | 6 | 6 0 0 3 0 | 2 0 0 0 3 0 0 | * 8N * * trip . o . x3*b4x . . | 24 | 0 24 24 0 0 | 0 8 6 0 0 12 0 | * * 2N * sirco . o . x3*b . . x | 6 | 0 6 0 0 3 | 0 2 0 0 0 0 3 | * * * 8N trip
© 2004-2024 | top of page |