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Cubic-octahedral Honeycomb
In the geometry of Hyperbolic space, hyperbolic 3-space, the cubic-octahedral honeycomb is a compact uniform honeycomb (geometry), honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter-Dynkin diagram, Coxeter diagram, , and is named by its two regular cells. Images Wide-angle perspective views: File:H3 4343-0010 center ultrawide.png, Centered on cube File:H3 4343-1000 center ultrawide.png, Centered on octahedron File:H3 4343-0001 center ultrawide.png, Centered on cuboctahedron It contains a subgroup H2 tiling, the alternated order-4 hexagonal tiling, , with vertex figure (3.4)4. : Symmetry A lower symmetry form, index 6, of this honeycomb can be constructed with [(4,3,4,3*)] symmetry, represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram . This lower symmetry can be extended by restoring one mirror as . Related honeycombs There are 5 related uniform honeycomb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Honeycombs In Hyperbolic Space
In hyperbolic geometry, a uniform honeycomb in hyperbolic space is a uniform tessellation of uniform polyhedron, uniform polyhedral Cell (geometry), cells. In 3-dimensional hyperbolic space there are nine Coxeter group families of compact convex uniform honeycombs, generated as Wythoff constructions, and represented by permutations of Coxeter-Dynkin diagram#Application with uniform polytopes, rings of the Coxeter diagrams for each family. Hyperbolic uniform honeycomb families Honeycombs are divided between compact and paracompact forms defined by Coxeter groups, the first category only including finite cells and vertex figures (finite subgroups), and the second includes affine subgroups. Compact uniform honeycomb families The nine compact Coxeter groups are listed here with their Coxeter diagrams, in order of the relative volumes of their Fundamental domain, fundamental simplex domains.Felikson, 2002 These 9 families generate a total of 76 unique uniform honeycombs. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with 1, unit s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboid
In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six Face (geometry), faces; it has eight Vertex (geometry), vertices and twelve Edge (geometry), edges. A ''rectangular cuboid'' (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a Convex polyhedron, convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the Dihedral angle, angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles. Along with the rectangular cuboids, ''parallelepiped'' is a cuboid with six parallelogram faces. ''Rhombohedron'' is a cuboid with six rhombus faces. A ''square fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform T02 4343 Honeycomb Verf
A uniform is a variety of costume worn by members of an organization while usually participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools, and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non-members to wear the uniform. Etymology From the Latin ''unus'' (meaning one), and ''forma'' (meaning form). Variants Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonal Trapezohedron
In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. The variety with rhombus-shaped faces faces is a rhombohedron. An alternative name for the same shape is the ''trigonal deltohedron''. Geometry Six identical rhombic faces can construct two configurations of trigonal trapezohedra. The ''acute'' or ''prolate'' form has three acute angle corners of the rhombic faces meeting at the two polar axis vertices. The ''obtuse'' or ''oblate'' or ''flat'' form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices. More strongly than having all faces congruent, the trigonal trapezohedra are isohedral figures, meaning that they have symmetries that take any face to any other face. Special cases A cube is a special case of a trigonal trapezohedron, since a square is a special case of a rhombus. A gyroelongated triangular bipyramid constructed with equilateral triangles can al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Tiling Verf 34343434
A uniform is a variety of costume worn by members of an organization while usually participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools, and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non-members to wear the uniform. Etymology From the Latin ''unus'' (meaning one), and ''forma'' (meaning form). Variants Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternated Order-4 Hexagonal Tiling
In geometry, the alternated order-4 hexagonal tiling is a Uniform tilings in hyperbolic plane, uniform tiling of the Hyperbolic geometry, hyperbolic plane. It has Schläfli symbol of (3,4,4), h, and hr. Uniform constructions There are four uniform constructions, with some of lower ones which can be seen with two colors of triangles: Related polyhedra and tiling References * John Horton Conway, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, ''The Symmetries of Things'' 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations) * See also *Square tiling *Uniform tilings in hyperbolic plane *List of regular polytopes External links * * Hyperbolic and Spherical Tiling Gallery * [http://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch] Hexagonal tilings Hyperbolic tilings Isogonal tilings Order-4 tilings Semiregular tilings {{hyperbolic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
