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The truncated cuboctahedron is an Archimedean solid. It has 12 regular square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges. Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated cuboctahedron is a zonohedron. Download high resolution version (855x868, 83 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ...
Spinning truncated tetrahedron, made by me using POV-Ray, see image:poly. ...
In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ...
It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ...
In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ...
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wijthoff, is a method for constructing a uniform polyhedron or plane tiling. ...
Coxeter groups in the plane with equivalent diagrams. ...
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// List of symmetry groups on the sphere Spherical symmetry groups are also called point groups (in 3D). ...
The octahedral rotation group O with fundamental domain Chiral and achiral octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. ...
A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...
A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...
H.S.M. Coxeter. ...
This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus J. Wenninger. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
A disdyakis dodecahedron, or hexakis octahedron, is the Catalan solid whose Archimedean dual is the truncated cuboctahedron. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
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In polyhedral geometry a vertex configuration is a short-hand notation for representing a vertex as the sequence of faces around a vertex. ...
Image File history File links Download high resolution version (638x639, 23 KB) Summary Great rhombicuboctahedron, U17 Licensing I, the creator of this work, hereby release it into the public domain. ...
Image File history File links Download high resolution version (638x639, 23 KB) Summary Great rhombicuboctahedron, U17 Licensing I, the creator of this work, hereby release it into the public domain. ...
Image File history File links Truncated_cuboctahedron_flat. ...
Image File history File links Truncated_cuboctahedron_flat. ...
Categories: Polyhedra | Stub ...
In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ...
For other uses, see square. ...
A regular hexagon. ...
For other uses, see Octagon (disambiguation). ...
A sphere rotating around its axis. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
Other names Alternate interchangeable names are: - Rhombitruncated cuboctahedron
- Great rhombicuboctahedron
- Omnitruncated cuboctahedron
The name truncated cuboctahedron, given originally by Johannes Kepler, is a little misleading. If you truncate a cuboctahedron by cutting the corners off, you do not get this uniform figure: some of the faces will be rectangles. However, the resulting figure is topologically equivalent to a truncated cuboctahedron and can always be deformed until the faces are regular. Johannes Kepler (December 27, 1571 – November 15, 1630) was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. ...
A truncated cube - faces double in sides, and vertices replaced by new faces. ...
In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ...
A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology. ...
The alternative name great rhombicuboctahedron refers to the fact that the 12 square faces lie in the same planes as the 12 faces of the rhombic dodecahedron which is dual to the cuboctahedron. Compare to small rhombicuboctahedron. The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. ...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. ...
One unfortunate point of confusion: There is a nonconvex uniform polyhedron by the same name. See uniform great rhombicuboctahedron. In geometry, the Uniform great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. ...
Cartesian coordinates Cartesian coordinates for the vertices of a truncated cuboctahedron centered at the origin are all permutations of Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
- (±1, ±(1+√2), ±(1+√8)). (edge length = 2)
See also Three dimensions A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. ...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ...
References - Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)
This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...
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