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The rectified order-5 hexagonal tiling honeycomb, t 1 {6,3,5}, has icosahedron and trihexagonal tiling facets, with a pentagonal prism vertex figure. It is similar to the 2D hyperbolic infinite-order square tiling, r{∞,5} with pentagon and apeirogonal faces. All vertices are on the ideal surface.
The truncated hexagonal tiling honeycomb, t 0,1 {6,3,3}, has tetrahedral and truncated hexagonal tiling facets, with a triangular pyramid vertex figure. It is similar to the 2D hyperbolic truncated order-3 apeirogonal tiling , t{∞,3} with apeirogonal and triangle faces:
The order-5 truncated pentagonal hexecontahedron is a convex polyhedron with 72 faces: 60 hexagons and 12 pentagons triangular, with 210 edges, and 140 vertices. Its dual is the pentakis snub dodecahedron. It is Goldberg polyhedron {5+,3} 2,1 in the icosahedral family, with chiral symmetry. The relationship between pentagons steps into 2 ...
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.There are 2 dodecagons (12-sides) and one triangle on each vertex.. As the name implies this tiling is constructed by a truncation operation applied to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations.
5 6 7 Rows of squares with horizontal offsets Rows of triangles with horizontal offsets A tiling by squares: Three hexagons surround each triangle Six triangles surround every hexagon. Three size triangles cmm (2*22) p2 (2222) cmm (2*22) p4m (*442) p6 (632) p3 (333) Hexagonal tiling Square tiling Truncated square tiling Truncated hexagonal tiling
In geometry, the truncated order-5 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t 0,1 {6,5}. Related polyhedra and tiling
The truncated order-5 cubic honeycomb, , has truncated cube and icosahedron cells, with a pentagonal pyramid vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-5 square tiling , t{4,5}, with truncated square and pentagonal faces:
The remaining 6 truncated cuboctahedra project to the (non-regular) octagonal faces of the envelope. These are connected to the central truncated cuboctahedron via 6 octagonal prisms, which are the images of the octagonal prism cells, a pair to each image. The 8 hexagonal faces of the envelope are the images of 8 of the hexagonal prisms.