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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 ...
Download QR code; Print/export ... Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. ... 5 / 4 .10.5: I h ...
Convex regular icosahedron. Let P and Q be combinatorially equivalent 3-dimensional convex polytopes; that is, they are convex polytopes with isomorphic face lattices.Suppose further that each pair of corresponding faces from P and Q are congruent to each other, i.e. equal up to a rigid motion.
Category:Uniform polyhedra includes subcategories below AND 53 nonconvex forms: Category:Platonic solids for the five convex regular polyhedra. Category:Kepler–Poinsot polyhedra for the four non-convex regular polyhedra. Category:Archimedean solids for the remaining convex semi-regular polyhedra, excluding prisms and antiprisms.
This version holds both for convex polyhedra (where the densities are all 1) and the non-convex Kepler–Poinsot polyhedra. Projective polyhedra all have Euler characteristic 1, like the real projective plane , while the surfaces of toroidal polyhedra all have Euler characteristic 0, like the torus .
A Johnson solid is a convex polyhedron whose faces are all regular polygons. [2] Here, a polyhedron is said to be convex if the shortest path between any two of its vertices lies either within its interior or on its boundary, none of its faces are coplanar (meaning they do not share the same plane, and do not "lie flat"), and none of its edges are colinear (meaning they are not segments of the ...
There are many relations among the uniform polyhedra. [1] [2] [3] Some are obtained by truncating the vertices of the regular or quasi-regular polyhedron.Others share the same vertices and edges as other polyhedron.
In geometry, a hexecontahedron (or hexacontahedron [1]) is a polyhedron with 60 faces. There are many symmetric forms, and the ones with highest symmetry have icosahedral symmetry: Four Catalan solids, convex: Pentakis dodecahedron - isosceles triangles; Deltoidal hexecontahedron - kites; Pentagonal hexecontahedron - pentagons