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In the geometry of three dimensions, a stellation extends a polyhedron to form a new figure that is also a polyhedron. The following is a list of stellations of various polyhedra. h The following is a list of stellations of various polyhedra. h
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
The following year, Arthur Cayley gave the Kepler–Poinsot polyhedra the names by which they are generally known today. A hundred years later, John Conway developed a systematic terminology for stellations in up to four dimensions. Within this scheme the small stellated dodecahedron is just the stellated dodecahedron.
The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors. The balls are "expanded" rhombicosidodecahedra, with the squares replaced ...
Construction of a stellated dodecagon: a regular polygon with Schläfli symbol {12/5}. In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.
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.
Its dual polyhedron is the great stellated dodecahedron { 5 / 2 , 3}, having three regular star pentagonal faces around each vertex. Stellated icosahedra Stellation is the process of extending the faces or edges of a polyhedron until they meet to form a new polyhedron.
Regular polyhedron. Platonic solid: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron; Abstract regular polyhedra (Projective polyhedron)