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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. It also ...
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.
Snub polyhedra have Wythoff symbol | p q r and by extension, vertex configuration 3.p.3.q.3.r.Retrosnub polyhedra (a subset of the snub polyhedron, containing the great icosahedron, small retrosnub icosicosidodecahedron, and great retrosnub icosidodecahedron) still have this form of Wythoff symbol, but their vertex configurations are instead (..).
A topological icosidodecahedron in truncated cube, inserting 6 vertices in center of octagons, and dissecting them into 2 pentagons and 2 triangles. The truncated cube can be turned into an icosidodecahedron by dividing the octagons into two pentagons and two triangles.
Conway calls Coxeter's operation a semi-snub. [2] In this notation, snub is defined by the dual and gyro operators, as s = dg, and it is equivalent to an alternation of a truncation of an ambo operator. Conway's notation itself avoids Coxeter's alternation (half) operation since it only applies for polyhedra with only even-sided faces.
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.
This uniform polyhedron compound is a composition of the 2 enantiomers of the great snub icosidodecahedron. References. Skilling, John (1976), ...