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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
To find the volume and surface area of a pentagonal hexecontahedron, denote the shorter side of one of the pentagonal faces as , and set a constant t [1] = + (+) + + () Then the surface area ( A {\displaystyle A} ) is: A = 30 b 2 ⋅ ( 2 + 3 t ) ⋅ 1 − t 2 1 − 2 t 2 ≈ 162.698 b 2 {\displaystyle A={\frac {30b^{2}\cdot (2+3t)\cdot {\sqrt ...
6.10 2: t{5,6} Truncated order-6 hexagonal tiling: 6.12 2: t{6,6} Truncated order-6 octagonal tiling: 6.16 2: t{8,6} Heptagonal tiling: 7 3 {7,3} Order-4 heptagonal ...
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.
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.
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