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In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces. The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles .
3D model of a snub icosidodecadodecahedron. In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U 46. It has 104 faces (80 triangles, 12 pentagons, and 12 pentagrams), 180 edges, and 60 vertices. [1] As the name indicates, it belongs to the family of snub polyhedra.
3D model of a great snub icosidodecahedron. In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 57. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. [1] It can be represented by a Schläfli symbol sr{5 ⁄ 2,3}, and Coxeter-Dynkin diagram.
In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 74. It has 92 faces (80 triangles and 12 pentagrams ), 150 edges, and 60 vertices. [ 1 ]
In four-dimensional geometry, the icosidodecahedron appears in the regular 600-cell as the equatorial slice that belongs to the vertex-first passage of the 600-cell through 3D space. In other words: the 30 vertices of the 600-cell which lie at arc distances of 90 degrees on its circumscribed hypersphere from a pair of opposite vertices, are the ...
In geometry, the great inverted snub icosidodecahedron (or great vertisnub icosidodecahedron) is a uniform star polyhedron, indexed as U 69. It is given a Schläfli symbol sr{5 ⁄ 3,3}, and Coxeter-Dynkin diagram. In the book Polyhedron Models by Magnus Wenninger, the polyhedron is misnamed great snub icosidodecahedron, and vice versa.
3D model of a small retrosnub icosicosidodecahedron. In geometry, the small retrosnub icosicosidodecahedron (also known as a retrosnub disicosidodecahedron, small inverted retrosnub icosicosidodecahedron, or retroholosnub icosahedron) is a nonconvex uniform polyhedron, indexed as U 72.
3D model of a small snub icosicosidodecahedron. In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U 32. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron.