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Rhombicosahedron
In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. It has 50 faces (30 squares and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is an antiparallelogram. Related polyhedra A rhombicosahedron shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) and the icosidodecadodecahedron (having the hexagonal faces in common). Rhombicosacron The rhombicosacron is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed by ..., and 60 crossed-quadrilateral faces. References * External links ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Twenty Triangular Prisms
This uniform polyhedron compound is a symmetric arrangement of 20 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron. It results from composing the two enantiomorphs In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be ... of the compound of 10 triangular prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two triangular prisms incident on each of its vertices. Related polyhedra This compound shares its vertex arrangement with three uniform polyhedra as follows: References *. Polyhedral compounds {{polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Ten Triangular Prisms
This uniform polyhedron compound is a Chirality (mathematics), chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron. Related polyhedra This compound shares its vertex arrangement with three uniform polyhedron, uniform polyhedra as follows: References *. Polyhedral compounds {{polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosidodecadodecahedron
In geometry, the icosidodecadodecahedron (or icosified dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U44. It has 44 faces (12 pentagons, 12 pentagrams and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is a crossed quadrilateral. Related polyhedra It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the hexagonal faces in common). See also * List of uniform polyhedra In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive ( transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are c ... * Snub icosidodecadodecahedron References External links * Uniform polyhedra {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombidodecadodecahedron Convex Hull
In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces (30 squares, 12 pentagons and 12 pentagrams), 120 edges and 60 vertices. It is given a Schläfli symbol t0,2, and by the Wythoff construction this polyhedron can also be named a '' cantellated great dodecahedron''. Cartesian coordinates Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of : (±1/τ2, 0, ±τ2) : (±1, ±1, ±) : (±2, ±1/τ, ±τ) where τ = (1+)/2 is the golden ratio (sometimes written φ). Related polyhedra It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the icosidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the square faces in common). Medial deltoidal hexecontahedron The medial deltoidal hexecontahedron (or midly lanceal ditria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosidodecadodecahedron
In geometry, the icosidodecadodecahedron (or icosified dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U44. It has 44 faces (12 pentagons, 12 pentagrams and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is a crossed quadrilateral. Related polyhedra It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the hexagonal faces in common). See also * List of uniform polyhedra In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive ( transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are c ... * Snub icosidodecadodecahedron References External links * Uniform polyhedra {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombidodecadodecahedron
In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces (30 squares, 12 pentagons and 12 pentagrams), 120 edges and 60 vertices. It is given a Schläfli symbol t0,2, and by the Wythoff construction this polyhedron can also be named a '' cantellated great dodecahedron''. Cartesian coordinates Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of : (±1/τ2, 0, ±τ2) : (±1, ±1, ±) : (±2, ±1/τ, ±τ) where τ = (1+)/2 is the golden ratio (sometimes written φ). Related polyhedra It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the icosidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the square faces in common). Medial deltoidal hexecontahedron The medial deltoidal hexecontahedron (or midly lanceal ditria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Ten Triangular Prisms
This uniform polyhedron compound is a Chirality (mathematics), chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron. Related polyhedra This compound shares its vertex arrangement with three uniform polyhedron, uniform polyhedra as follows: References *. Polyhedral compounds {{polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonconvex Uniform Polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra includes the 4 regular ones, called the Kepler–Poinsot polyhedra, 5 quasiregular ones, and 48 semiregular ones. There are also two infinite sets of ''uniform star prisms'' and ''uniform star antiprisms''. Just as (nondegenerate) star polygons (which have polygon density greater than 1) correspond to circular polygons with overlapping tiles, star polyhedra that do not pass through the center have polytope density greater than 1, and correspond to spherical polyhedra with overlapping tiles; there are 47 nonprismatic such uniform star polyhedra. The remaining 10 nonprismatic uniform star polyhedra, those that pass through the center, are the hemipolyhedra as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossed-quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, derived from greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A, B, C and D is sometimes denoted as \square ABCD. Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ''ABCD'' add up to 360 degrees of arc, that is :\angle A+\angle B+\angle C+\angle D=360^. This is a special case of the ''n''-gon interior angle sum formula: ''S'' = (''n'' − 2) × 180°. All non-self-crossing quadrilaterals tile the plane, by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
