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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.
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.
Truncated order-5 square tiling: 5.8 2: t{4,5} Truncated order-5 pentagonal tiling: 5.10 2: t{5,5} Truncated order-5 hexagonal tiling: 5.12 2: t{6,5} Pentaapeirogonal ...
The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 287, pentagonal hexecontahedron )
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
These 12 order-5 vertices can be truncated such that all edges are equal length. The original 30 rhombic faces become non-regular hexagons, and the truncated vertices become regular pentagons. The hexagon faces can be equilateral but not regular with D 2 symmetry.
Truncated order-5 pentagonal tiling; Truncated order-6 pentagonal tiling This page was last edited on 13 March 2023, at 09:40 (UTC). Text is ...