Crossed Square Cupola

picture info	Crossed Square Cupola In geometry, the crossed square cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to the convex square cupola. It can be obtained as a slice of the nonconvex great rhombicuboctahedron or quasirhombicuboctahedron. As in all cupolae, the base polygon has twice as many edges and vertices as the top; in this case the base polygon is an octagram. It may be seen as a cupola with a retrograde square base, so that the squares and triangles connect across the bases in the opposite way to the square cupola, hence intersecting each other. Related polyhedra The crossed square cupola may be seen as a part of some uniform polyhedra. For example, the great cubicuboctahedron may be seen as six crossed square cupolae connected at their triangular faces, while the nonconvex great rhombicuboctahedron may be seen as a blend of six cupolae. Additionally, the nonconvex great rhombicuboctahedron may be seen as an octagrammic prism with the octagrams excavate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Johnson Solid In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), vertex. An example of a Johnson solid is the square-based Pyramid (geometry), pyramid with equilateral sides (square pyramid, ); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform polyhedron, uniform (i.e., not Platonic solid, Archimedean solid, prism (geometry), uniform prism, or uniform antiprism) before they refer to it as a “Johnson solid”. As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex. The pentagonal pyramid () is an example that has a degree-5 vertex. Although there is no obvious restriction tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Pseudo-great Rhombicuboctahedron In geometry, the pseudo great rhombicuboctahedron is one of the two pseudo uniform polyhedra, the other being the convex elongated square gyrobicupola or pseudo rhombicuboctahedron. It has the same vertex figure as the nonconvex great rhombicuboctahedron (a uniform polyhedron), but is not a uniform polyhedron (due to not being isogonal), and has a smaller symmetry group. It can be obtained from the great rhombicuboctahedron by taking a square face and the 8 faces with a common vertex to it (forming a crossed square cupola) and rotating them by an angle of . It is related to the nonconvex great rhombicuboctahedron In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by the Schläfli symbol rr and Coxeter-Dynkin dia ... in the same way that the pseudo rhombicuboctahedron is related to the rhombicuboctahedron. Related polyhedra The pseud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Excavated Octagrammic Prism B Excavation may refer to: * Excavation (archaeology) * Excavation (medicine) * ''Excavation'' (The Haxan Cloak album), 2013 * ''Excavation'' (Ben Monder album), 2000 * ''Excavation'' (novel), a 2000 novel by James Rollins * '' Excavation: A Memoir'', a 2014 memoir by Wendy C. Ortiz * ''Excavation'' (video game), a 2003 video game by WildTangent See also Excavate (other) Excavator (other) * Excavata, a taxonomic grouping of eukaryotic unicellular organisms ''Celaenia excavata ''Celaenia excavata'', the bird dropping spider of Australia and New Zealand, derives its name from mimicking bird droppings to avoid predators, mainly birds. However, there are other species of spider that resemble bird droppings, for example s ... '', a spider {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Octahedral Symmetry A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the polyhedron that is dual polyhedron, dual to an octahedron. The group of orientation-preserving symmetries is ''S''4, the symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the cube. Details Chiral and full (or achiral) octahedral symmetry are the Point groups in three dimensions, discrete point symmetries (or equivalently, List of spherical symmetry groups, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. They are among the Crystal system#Overview of point groups by crystal system, crystallographic point groups of the cubic crystal system. As the hyperoctahedral group of dimension 3 the full oct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Excavated Octagrammic Prism A Excavation may refer to: * Excavation (archaeology) * Excavation (medicine) * ''Excavation'' (The Haxan Cloak album), 2013 * ''Excavation'' (Ben Monder album), 2000 * ''Excavation'' (novel), a 2000 novel by James Rollins * '' Excavation: A Memoir'', a 2014 memoir by Wendy C. Ortiz * ''Excavation'' (video game), a 2003 video game by WildTangent See also Excavate (other) Excavator (other) * Excavata, a taxonomic grouping of eukaryotic unicellular organisms ''Celaenia excavata ''Celaenia excavata'', the bird dropping spider of Australia and New Zealand, derives its name from mimicking bird droppings to avoid predators, mainly birds. However, there are other species of spider that resemble bird droppings, for example s ... '', a spider {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Elongated Square Cupola In geometry, the elongated square cupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a square cupola () by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" (another square cupola) removed. Formulae The following formulae for volume, surface area and circumscribed sphere, circumradius can be used if all face (geometry), faces are regular polygon, regular, with edge length ''a'': :V=\left(3+\frac\right)a^3\approx6.77124...a^3 :A=\left(15+2\sqrt+\sqrt\right)a^2\approx19.5605...a^2 :C=\left(\frac\sqrt\right)a\approx1.39897...a Dual polyhedron The dual of the elongated square cupola has 20 faces: 8 isosceles triangles, 4 kites, 8 quadrilaterals. Related polyhedra and honeycombs The elongated square cupola forms space-filling Honeycomb (geometry), honeycombs with Tetrahedron, tetrahedra and cubes; with cubes and Cuboctahedron, cuboctahedra; and with tetrahedra, elongated squ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Prism 8-3 Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary deposit * Prism correction, a component of some eyeglass prescriptions Government * PRISM, a surveillance program run by the US National Security Agency * PRISM (website), an educational portal website for Indiana teachers * Oregon Performance Reporting Information System, a state agency Media and entertainment Publications * Prism (comics), a Marvel Comics character * ''Prism International'', a Canadian literary magazine * ''PRism'' (journal), an academic journal covering public relations * ''ASEE Prism'', the flagship publication of the American Society for Engineering Education * Prism Comics, an organization that supports LGBT people in the comics industry * ''The Prism Pentad'', a series of Dungeons & Dragons novels by Troy Den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Great Rhombihexahedron In geometry, the great rhombihexahedron (or great rhombicube) is a nonconvex uniform polyhedron, indexed as U21. It has 18 faces (12 squares and 6 octagrams), 48 edges, and 24 vertices. Its dual is the great rhombihexacron. Its vertex figure is a crossed quadrilateral. Orthogonal projections Gallery Related polyhedra It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having 12 square faces in common), and with the great cubicuboctahedron (having the octagrammic faces in common). It may be constructed as the exclusive or (blend) of three octagrammic prisms. Similarly, the small rhombihexahedron may be constructed as the exclusive or of three octagonal prisms. Great rhombihexacron The great rhombihexacron is a nonconvex isohedral polyhedron. It is the dual of the uniform great rhombihexahedron (U21). It has 24 identical bow-tie-shaped faces, 18 vertices, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Great Cubicuboctahedron In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices. Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name ''cubicuboctahedron''. The ''great'' suffix serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions. Orthographic projections Related polyhedra It shares the vertex arrangement with the convex truncated cube and two other nonconvex uniform polyhedra. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having the octagrammic faces in common). Great hexacronic icositetrahedron The great hexacronic icositetrahedron (or great lanceal disdodecahedron) is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Pseudo-great Rhombicuboctahedron In geometry, the pseudo great rhombicuboctahedron is one of the two pseudo uniform polyhedra, the other being the convex elongated square gyrobicupola or pseudo rhombicuboctahedron. It has the same vertex figure as the nonconvex great rhombicuboctahedron (a uniform polyhedron), but is not a uniform polyhedron (due to not being isogonal), and has a smaller symmetry group. It can be obtained from the great rhombicuboctahedron by taking a square face and the 8 faces with a common vertex to it (forming a crossed square cupola) and rotating them by an angle of . It is related to the nonconvex great rhombicuboctahedron In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by the Schläfli symbol rr and Coxeter-Dynkin dia ... in the same way that the pseudo rhombicuboctahedron is related to the rhombicuboctahedron. Related polyhedra The pseud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Nonconvex Great Rhombicuboctahedron In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by the Schläfli symbol rr and Coxeter-Dynkin diagram of . Its vertex figure is a crossed quadrilateral. This model shares the name with the convex ''great rhombicuboctahedron'', also called the truncated cuboctahedron. An alternative name for this figure is quasirhombicuboctahedron. From that derives its Bowers acronym: querco. Orthographic projections Cartesian coordinates Cartesian coordinates for the vertices of a ''nonconvex great rhombicuboctahedron'' centered at the origin with edge length 1 are all the permutations of : (±''ξ'', ±1, ±1), where ''ξ'' = − 1. Related polyhedra It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement In geometry, a vertex arrangement is a set of points in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]