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Great Stellated 120-cell
In geometry, the great stellated 120-cell or great stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol . It is one of 10 regular Schläfli-Hess polytopes. It is one of four ''regular star 4-polytopes'' discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids. Related polytopes It has the same edge arrangement as the grand 600-cell, icosahedral 120-cell, and the same face arrangement as the grand stellated 120-cell. With its dual, it forms the compound of grand 120-cell and great stellated 120-cell. See also * List of regular polytopes * Convex regular 4-polytope * Kepler-Poinsot solids - regular star polyhedron * Star polygon - regular star polygons References * Edmund Hess, (1883) ''Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder' * Coxeter, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ortho Solid 012-uniform Polychoron P35-t0
Ortho- is a Greek prefix meaning “straight”, “upright”, “right” or “correct”. Ortho may refer to: * Ortho, Belgium, a village in the Belgian province of Luxembourg In science * arene substitution patterns, two substituents that occupy adjacent positions on an aromatic ring * Chlordane, an organochlorine compound that was used as a pesticide In mathematics: * Orthogonal, a synonym for perpendicular * Orthonormal, the property that a collection of vectors are mutually perpendicular and each of unit magnitude * Orthodrome, a synonym for great circle, a geodesic on the sphere * Orthographic projection, a parallel projection onto a perpendicular plane In medicine: * Orthomyxovirus, a family of viruses to which influenza belongs * Orthodontics, a specialty of dentistry concerned with the study and treatment of malocclusions * Orthopedic, the study of the musculoskeletal system * Ortho-DOT, a psychedelic drug * Ortho-cept and Ortho Tri-cyclen, kinds of oral cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example, a ''square vertex arrangement'' is understood to mean four points in a plane, equal distance and angles from a center point. Two polytopes share the same ''vertex arrangement'' if they share the same 0-skeleton. A group of polytopes that shares a vertex arrangement is called an ''army''. Vertex arrangement The same set of vertices can be connected by edges in different ways. For example, the ''pentagon'' and ''pentagram'' have the same ''vertex arrangement'', while the second connects alternate vertices. A ''vertex arrangement'' is often described by the convex hull polytope which contains it. For example, the regular ''pentagram'' can be said to have a (regular) ''pentagonal vertex arrangement''. Infinite tilings can also share common ''vertex arrangements''. For example, this triangular lattice of point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Polyhedron
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: *Polyhedra which self-intersect in a repetitive way. *Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way. Mathematically these figures are examples of star domains. Mathematical studies of star polyhedra are usually concerned with regular, uniform polyhedra, or the duals of the uniform polyhedra. All these stars are of the self-intersecting kind. Self-intersecting star polyhedra Regular star polyhedra The regular star polyhedra are self-intersecting polyhedra. They may either have self-intersecting faces, or self-intersecting vertex figures. There are four regular star polyhedra, known as the Kepler–Poinsot polyhedra. The Schläfli symbol implies faces with ''p'' sides, and vertex figures with ''q'' sides. Two of them have pentag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Regular 4-polytope
In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. History The convex regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. He discovered that there are precisely six such figures. Schläfli also found four of the regular star 4-polytopes: the grand 120-cell, great stellated 120-cell, grand 600-cell, and great grand stellated 120-cell. He skipped the remaining six because he would not allow forms that failed the Euler characteristic on cells or vertex figures (for zero-hole tori: ''F'' − ''E'' + ''V'' 2). That excludes cells and vertex figures such as the great dodecahedron and small stellated dodecahedron . Edmund Hess (1843–1903) publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
