In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
[citation needed] Another convex polyhedron is formed by the small central space common to all members of the compound.
Coxeter's notation for regular compounds is given in the table above, incorporating Schläfli symbols.
The material inside the square brackets, [d{p,q}], denotes the components of the compound: d separate {p,q}'s.
The hull is the dual of this rectification, and its rhombic faces have the intersecting edges of the two solids as diagonals (and have their four alternate vertices).
The octahedral and icosahedral dual compounds are the first stellations of the cuboctahedron and icosidodecahedron, respectively.
The section for enantiomorph pairs in Skilling's list does not contain the compound of two great snub dodecicosidodecahedra, as the pentagram faces would coincide.
There are eighteen two-parameter families of regular compound tessellations of the Euclidean plane.
In the hyperbolic plane, five one-parameter families and seventeen isolated cases are known, but the completeness of this listing has not been enumerated.
The Euclidean and hyperbolic compound families 2 {p,p} (4 ≤ p ≤ ∞, p an integer) are analogous to the spherical stella octangula, 2 {3,3}.