Snub cube
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Type	Archimedean
Faces	32 triangles 6 squares
Edges	60
Vertices	24
Vertex configuration	3,3,3,3,4
Symmetry group	octahedral (O)
Dual polyhedron	pentagonal icositetrahedron
Properties	convex, semi-regular (vertex-uniform), chiral

The snub cube, or snub cuboctahedron, is an Archimedean solid. Download high resolution version (837x817, 96 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (843x833, 97 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning truncated tetrahedron, 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. ... Jump to: navigation, search A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. ... A square as a geometric shape is described and illustrated at square (geometry). ... The symmetry group of an object (e. ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... A pentagonal icositetrahedron is a catalan solid which looks a bit like an octahedron undergoing cell division. ... In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. ... 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. ...

The snub cube has 38 faces, of which 6 are squares and the other 32 are equilateral triangles. It has 60 edges and 24 vertices. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. In plane geometry, a square is a polygon with four equal sides and equal angles. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... Mirror Image is an episode of the television series The Twilight Zone. ... Chirality refers to several phenomena, all having to do with objects that differ from their mirror image. ...

Canonical coordinates

Canonical coordinates for a snub cube are all the even permutations of (±1, ±ξ, ±1/ξ) with an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where ξ is the real solution to ξ³+ξ²+ξ=1, which can be written In physics, the canonical commutation relation is the relation among the position and momentum of a point particle in one dimension, where is the so-called commutator of and , is the imaginary unit and is the reduced Plancks constant. ...

or approximately 0.543689. Taking the even permutations with an odd number of plus signs, and the odd permutations with an even number of plus signs gives a different snub cube, the mirror image.

Geometric relations

The snub cube can be generated by taking the six faces of the cube, pulling them outward so they no longer touch. Then give them all a small rotation on their centers (all clockwise or all counter-clockwise) until the space between can be filled by triangles.

The snub cube should not be confused with the truncated cube. The truncated cube, or truncated hexahedron, is an Archimedean solid. ...

Image File history File links Flattened polyhedron, source is image:makepolys. ...

See also

• snub dodecahedron

The snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, usually regarded as a truncated polyhedron derived by truncating either a dodecahedron or an icosahedron. ...

External links

• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra