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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 .
Snub is a construction process of polyhedra by separating the polyhedron faces, twisting their faces in certain angles, and filling them up with equilateral triangles. Examples can be found in snub cube and snub dodecahedron .
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]
In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus simus) and snub dodecahedron (dodecaedron simum). [1] In general, snubs have chiral symmetry with two forms: with clockwise or counterclockwise orientation.
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 ...
The snub 24-cell and grand antiprism were missing from her list. [ 3 ] 1911 : Pieter Hendrik Schoute published Analytic treatment of the polytopes regularly derived from the regular polytopes , followed Boole-Stott's notations, enumerating the convex uniform polytopes by symmetry based on 5-cell , 8-cell / 16-cell , and 24-cell .
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 .
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 ...