Compound of two snub cubes
The disnub cuboctahedron, disco, or compound of two snub cubes is a uniform polyhedron compound. It consists of 48 snub triangles, 16 further triangles, and 12 squares (the latter two can combine in pairs due to faces in the same plane). Four triangles and one square join at each vertex.
Compound of two snub cubes | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Disco |
Coxeter diagram | ß4ß3ß () |
Elements | |
Components | 2 snub cubes |
Faces | 48 triangles, 16 triangles as 8 hexagrams, 12 squares as 6 stellated octagons |
Edges | 24+48+48 |
Vertices | 48 |
Vertex figure | Floret pentagon, edge lengths 1, 1, 1, 1, √2 |
Measures (edge length 1) | |
Circumradius | ≈ 1.34371 |
Volume | ≈ 15.77896 |
Dihedral angles | 3–3: ≈ 153.23459° |
4–3: ≈ 142.98343° | |
Central density | 2 |
Number of external pieces | 160 |
Level of complexity | 26 |
Related polytopes | |
Army | Semi-uniform Girco |
Regiment | Disco |
Dual | Compound of two pentagonal icositetrahedra |
Conjugate | Compound of two snub cubes |
Convex core | Cuboctatruncated disdyakis dodecahedron |
Abstract & topological properties | |
Flag count | 480 |
Orientable | Yes |
Properties | |
Symmetry | B_{3}, order 48 |
Flag orbits | 10 |
Convex | No |
Nature | Tame |
Its quotient prismatic equivalent is the snub cubic antiprism, which is four-dimensional.
Measures edit
The circumradius R ≈ 1.34371 of the disnub cuboctahedron with unit edge length is the largest real root of
Its volume V ≈ 15.77896 is given by the largest real root of
- .
Its dihedral angles can be given as acos(α) for the angle between two triangular faces, and acos(β) for the angle between a square face and a triangular face, where α ≈ –0.89286 equals the unique real root of
and β ≈ –0.79846 equals the unique negative real root of
- ^{[1]}
Vertex coordinates edit
A disnub cuboctahedron of edge length 1 has coordinates given by all permutations of:
- (±c_{1}, ±c_{2}, ±c_{3}),
where
External links edit
- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#68).
- Klitzing, Richard. "disco".
- Wikipedia contributors. "Compound of two snub cubes".
- ↑ Wolfram Research, Inc. (2024). "Wolfram|Alpha Knowledgebase". Champaign, IL. "
PolyhedronData["SnubCube", {"Circumradius", "Volume", "DihedralAngles"}]
".