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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 ...
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.
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
In geometry, the chamfered truncated icosahedron is a convex polyhedron with 240 vertices, 360 edges, and 122 faces, 110 hexagons and 12 pentagons. It is constructed by a chamfer operation to the truncated icosahedron , adding new hexagons in place of original edges.
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
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.
In geometry, the truncated hexagonal trapezohedron is the fourth in an infinite series of truncated trapezohedra. It has 12 pentagon and 2 hexagon faces. It can be constructed by taking a hexagonal trapezohedron and truncating the polar axis vertices.
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.