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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 .
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U 40. It has 84 faces (60 triangles , 12 pentagons , and 12 pentagrams ), 150 edges, and 60 vertices. [ 1 ] It is given a Schläfli symbol sr{ 5 ⁄ 2 ,5}, as a snub great dodecahedron .
It is explicitly called a pentatruncated pentagonal hexecontahedron since only the valence-5 vertices of the pentagonal hexecontahedron are truncated. [2]Its topology can be constructed in Conway polyhedron notation as t5gD and more simply wD as a whirled dodecahedron, reducing original pentagonal faces and adding 5 distorted hexagons around each, in clockwise or counter-clockwise forms.
Net (click to enlarge) The pentakis snub dodecahedron is a convex polyhedron with 140 triangular faces, 210 edges, and 72 vertices. It has chiral icosahedral symmetry ...
Pentagonal pyramids are added to the 12 pentagonal faces of the snub dodecahedron, and triangular pyramids are added to the 20 triangular faces that do not share an edge with a pentagon. The pyramid heights are adjusted to make them coplanar with the other 60 triangular faces of the snub dodecahedron. The result is the pentagonal ...
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.
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 (..).
The snub disphenoid name comes from Johnson (1966) classification of the Johnson solid. [12] However, this solid was first studied by Rausenberger (1915). [13] [14] It was studied again in the paper by Freudenthal & van d. Waerden (1947), which first described the set of eight convex deltahedra, and named it the Siamese dodecahedron. [15] [14]