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Order-3-5 Heptagonal Honeycomb
In the geometry of Hyperbolic space, hyperbolic 3-space, the order-3-5 heptagonal honeycomb a regular space-filling tessellation (or honeycomb (geometry), honeycomb). Each infinite cell consists of a heptagonal tiling whose vertices lie on a Hypercycle (geometry), 2-hypercycle, each of which has a limiting circle on the ideal sphere. Geometry The Schläfli symbol of the order-3-5 heptagonal honeycomb is , with five heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is an icosahedron, . Related polytopes and honeycombs It is a part of a series of regular polytopes and honeycombs with Schläfli symbol, and icosahedral vertex figures. Order-3-5 octagonal honeycomb In the geometry of Hyperbolic space, hyperbolic 3-space, the order-3-5 octagonal honeycomb a regular space-filling tessellation (or honeycomb (geometry), honeycomb). Each infinite cell consists of an octagonal tiling whose vertices lie on a Hypercycle (geometry), 2-hypercycle, each of w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Regular Polytopes
This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. Overview This table shows a summary of regular polytope counts by rank. There are no Euclidean regular star tessellations in any number of dimensions. 1-polytopes There is only one polytope of rank 1 (1-polytope), the closed line segment bounded by its two endpoints. Every realization of this 1-polytope is regular. It has the Schläfli symbol , or a Coxeter diagram with a single ringed node, . Norman Johnson calls it a ''dion'' and gives it the Schläfli symbol . Although trivial as a polytope, it appears as the edges of polygons and other higher dimensional polytopes. It is used in the definition of uniform prisms like Schläfli symbol ×, or Coxeter diagram as a Cartesian product of a line segment and a regular polygon. 2-polytopes (polygons) The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A -gonal regular polygon is repre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
