Snub cube
Archimedean solid with 38 faces / From Wikipedia, the free encyclopedia
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In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.
This article includes a list of general references, but it lacks sufficient corresponding inline citations. (January 2012) |
Snub cube | |
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(Click here for rotating model) | |
Type | Archimedean solid Uniform polyhedron |
Elements | F = 38, E = 60, V = 24 (χ = 2) |
Faces by sides | (8+24){3}+6{4} |
Conway notation | sC |
Schläfli symbols | sr{4,3} or |
ht0,1,2{4,3} | |
Wythoff symbol | | 2 3 4 |
Coxeter diagram | |
Symmetry group | O, 1/2B3, [4,3]+, (432), order 24 |
Rotation group | O, [4,3]+, (432), order 24 |
Dihedral angle | 3-3: 153°14′04″ (153.23°) 3-4: 142°59′00″ (142.98°) |
References | U12, C24, W17 |
Properties | Semiregular convex chiral |
Colored faces |
3.3.3.3.4 (Vertex figure) |
Pentagonal icositetrahedron (dual polyhedron) |
Net |
It is a chiral polyhedron; that is, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two snub cubes, and the convex hull of both sets of vertices is a truncated cuboctahedron.
Kepler first named it in Latin as cubus simus in 1619 in his Harmonices Mundi. H. S. M. Coxeter, noting it could be derived equally from the octahedron as the cube, called it snub cuboctahedron, with a vertical extended Schläfli symbol , and representing an alternation of a truncated cuboctahedron, which has Schläfli symbol .