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In geometry, the snub disphenoid or dodecadeltahedron is a dodecahedron and one of the Johnson solids (''J''84). It is a three-dimensional solid that has only equilateral triangles as faces, and is therefore a deltahedron. It is not a regular polyhedron because some vertices have four faces and others have five. It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. The ''snub disphenoid'' is constructed, as its name suggests, as a snub disphenoid, and represented as ss, with s as a digonal antiprism, being the first of an infinite set of snub antiprisms. This construction also produces two degenerate digonal faces from the digonal antiprism.〔(Snub Anti-Prisms )〕 |- |160px |160px |- !Digonal antiprism (disphenoid) !Snub disphenoid |} It can also be seen as the 8 triangular faces of the square antiprism with the two squares replaced by pairs of triangles. It was called a Siamese dodecahedron in the paper by Freudenthal and van der Waerden which first described it in 1947 in the set of eight convex deltahedra. The snub disphenoid is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size. The other three polyhedra with this property are the regular octahedron, the pentagonal bipyramid, and an irregular polyhedron with 12 vertices and 20 triangular faces . The snub disphenoid has three dihedral angles, approximately 121.7°, 96.2°, 166.4°. == References == * *. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「snub disphenoid」の詳細全文を読む スポンサード リンク
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