Acronym | ... |
Name | hyperbolic honeycomb o6o5x∞xØx∞*c *b3*e |
Circumradius | sqrt[-5+2 sqrt(5)]/2 = 0.363271 i |
Vertex figure | ofx6ooo&#ut |
Confer |
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Both hyperbolic honeycombs o6o5x∞x3*b and x∞x5o6o have the same curvature and both use the same order 6 pentagonal tiling (hipat) as some of their bollocells. Thence it still can be blended out by an according overlay. Since the vertex figure of the former is a hexagonal frustrum xf6oo&#u and that of the latter is a hexagonal pyramid of6oo&#u, the one in here becomes the tegum sum of 3 within mutually 60° arranged, axially-intersecting u-scaled regular pentagons. Thus it clearly is still circumscribable, just as generally required for vertex figures of uniform polytopes, and thus moreover is convex. This in turn shows, that the two laminates of trats and dazatrapeats (from the first honeycomb) and of topazats (from the second honeycomb) attach as disjunct laminates (and won't pleat back).
Incidence matrix according to Dynkin symbol
o6o5x∞xØx∞*c *b3*e (N,M,K,L,P,Q → ∞) . . . . . | 10NMKLPQ | 6 1 6 | 6 6 6 6 | 1 6 6 -------------------+----------+---------------------------+-----------------------------------+-------------------- . . x . . | 2 | 30NMKLPQ * * | 2 0 1 1 | 0 2 2 . . . x . | 2 | * 5NMKLPQ * | 0 0 6 0 | 0 6 0 . . . . x | 2 | * * 30NMKLPQ | 0 2 0 1 | 1 0 2 -------------------+----------+---------------------------+-----------------------------------+-------------------- . o5x . . | 5 | 5 0 0 | 12NMKLPQ * * * | 0 1 1 . o . . x *b3*e | 3 | 0 0 3 | * 20NMKLPQ * * | 1 0 1 . . x∞x . ♦ 2M | M M 0 | * * 30NKLPQ * | 0 2 0 . . x . x∞*c ♦ 2K | K 0 K | * * * 30NMLPQ | 0 0 2 -------------------+----------+---------------------------+-----------------------------------+-------------------- o6o . . x *b3*e ♦ L | 0 0 3L | 0 2L 0 0 | 10NMKPQ * * . o5x∞x . ♦ 10MP | 10MP 5MP 0 | 2MP 0 10P 0 | * 6NKLQ * . o5x . x∞*c *b3*e ♦ 15KQ | 15KQ 0 15KQ | 3KQ 5KQ 0 15Q | * * 4NMLP
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