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Snub Cube | bgcolor=#e7dcc3 colspan=2|Snub cube | lign=center colspan=2|
Click on picture for large version.
Click here for spinning version. | lign=center colspan=2|
Click on picture for large version.
Click here for spinning version. | | gcolor=#e7dcc3|Type | Archimedean | | gcolor=#e7dcc3|Faces | 32 triangles
6 squares | | gcolor=#e7dcc3|Edges | 60 | | gcolor=#e7dcc3|Vertices | 24 | | gcolor=#e7dcc3|Vertex configuration | 3,3,3,3,4 | | gcolor=#e7dcc3|Symmetry group | octahedral (O) | | gcolor=#e7dcc3|Dual polyhedron | pentagonal icositetrahedron | | gcolor=#e7dcc3|Properties | convex, semi-regular (vertex-uniform), chiral | The snub cube, or snub cuboctahedron, is an Archimedean solid, usually regarded as a truncated polyhedron derived by truncating either a cube or an octahedron. 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. In three-dimensional space, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. In higher-dimensional spaces, these are congruent. 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 -
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. The snub cube should not be confused with the truncated cube. See also External links
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