Dual-regular Compounds
A dual-regular compound is composed of a regular polyhedron (one of the Platonic solids or Kepler-Poinsot polyhedra) and its regular dual, arranged reciprocally about a common intersphere or midsphere, such that the edge of one polyhedron intersects the dual edge of the dual polyhedron. There are five such compounds.
| Components | Picture | Convex hull | Core | Symmetry |
|---|---|---|---|---|
| Compound of two tetrahedra, or Stella octangula | Cube | Octahedron | *432 Oh |
|
| Compound of cube and octahedron | Rhombic dodecahedron | Cuboctahedron | *432 Oh |
|
| Compound of dodecahedron and icosahedron | Rhombic triacontahedron | Icosidodecahedron | *532 Ih |
|
| Compound of great icosahedron and great stellated dodecahedron | Dodecahedron | Icosahedron | *532 Ih |
|
| Compound of small stellated dodecahedron and great dodecahedron | Icosahedron | Dodecahedron | *532 Ih |
The dual-regular compound of a tetrahedron with its dual polyhedron is also the regular Stella octangula, since the tetrahedron is self-dual.
The cube-octahedron and dodecahedron-icosahedron dual-regular compounds are the first stellations of the cuboctahedron and icosidodecahedron, respectively.
The compound of the small stellated dodecahedron and great dodecahedron looks outwardly the same as the small stellated dodecahedron, because the great dodecahedron is completely contained inside. For this reason, the image shown above shows the small stellated dodecahedron in wireframe.
Read more about this topic: Polyhedral Compound
Famous quotes containing the word compounds:
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