Snub cube

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The snub cube, or snub cuboctahedron, is an Archimedean solid.

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.

Cartesian coordinates

Cartesian 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

[\xi = \frac\left(\sqrt[3]} - \sqrt[3]} - 1\right)]

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 spaces between can be filled with equilateral triangles.

The snub cube should not be confused with the truncated cube.

See also

• snub dodecahedron

External links

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

 

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