Search results
Results from the WOW.Com Content Network
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 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 ...
Order-5 hexagonal tiling Poincaré disk model of the hyperbolic plane: Type: Hyperbolic regular tiling: Vertex configuration: 6 5: Schläfli symbol {6,5} Wythoff symbol: 5 | 6 2 Coxeter diagram: Symmetry group [6,5], (*652) Dual: Order-6 pentagonal tiling: Properties: Vertex-transitive, edge-transitive, face-transitive
Truncated order-5 hexagonal tiling Poincaré disk model of the hyperbolic plane: Type: Hyperbolic uniform tiling: Vertex configuration: 5.12.12 Schläfli symbol: t{6,5} Wythoff symbol: 2 5 | 6 Coxeter diagram: Symmetry group [6,5], (*652) Dual: Order-6 pentakis pentagonal tiling: Properties: Vertex-transitive
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:
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
From a Wythoff construction there are fourteen hyperbolic uniform tilings that can be based from the regular order-5 hexagonal tiling. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are seven forms with full [6,5] symmetry, and three with subsymmetry.
In geometry, the truncated order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of t 0,1 {5,5}, constructed from one pentagons and two decagons around every vertex.