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3D model of a great stellated dodecahedron. In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5 ⁄ 2,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.
This shape also has alternative names called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron. The applications of snub disphenoid can be visualized as an atom cluster surrounding a central atom, that is the dodecahedral molecular geometry .
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Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the pentagrammic faces in common), the great ditrigonal icosidodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.
Gyroelongated triangular bicupola; Gyroelongated triangular cupola; Hebesphenomegacorona; Metabiaugmented dodecahedron; Metabiaugmented hexagonal prism; Metabiaugmented truncated dodecahedron; Metabidiminished icosahedron; Metabidiminished rhombicosidodecahedron; Metabigyrate rhombicosidodecahedron; Metagyrate diminished rhombicosidodecahedron
Animated truncation sequence from {5 ⁄ 2, 3} to {3, 5 ⁄ 2}The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 (hidden) pentagonal faces as truncations of the original pentagram faces, the latter forming a great dodecahedron inscribed within and sharing the edges of the icosahedron.
Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex)