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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 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 elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
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:
A hexagonal pyramid has seven vertices, twelve edges, and seven faces. One of its faces is hexagon, a base of the pyramid; six others are triangles. Six of the edges make up the pentagon by connecting its six vertices, and the other six edges are known as the lateral edges of the pyramid, meeting at the seventh vertex called the apex.
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.
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
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.