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There are a number of attractive polyhedron compounds consisting of seven octahedra. The compound illustrated above can be constructed as the dual of cube 7-compound. The ...

There are a number of attractive polyhedron compounds consisting of nine octahedra. The compound illustrated above can be constructed as the dual of cube 9-compound. The ...

Using either the fully supported or Miller's rules criterion (Webb), the octahedron has two reflexible stellations: the octahedron itself and the stella octangula.

A polycube composed of 5 cubes. There are 29 distinct three-dimensional pentacubes (Bouwkamp 1981). Of these, the 12 planar pentacubes (corresponding to solid pentominoes), ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...

The pentagonal rotunda is a convex polyhedron consisting of half of an icosidodecahedron, with the base being filled in by a decagon. It has 10 triangular and five pentagonal ...

The polyhedral formula generalized to a surface of genus g, V-E+F=chi(g) where V is the number of polyhedron vertices, E is the number of polyhedron edges, F is the number of ...

A polygrammic prism is a prism formed by two regular polygrams offset along their symmetry axis and with corresponding edges connected by lateral faces. The hexagrammic prism ...

A point at which three or more polyhedron edges of a polyhedron meet. The concept can also be generalized to a polytope.

There are 10 stellated regular 4-polytopes (Wells 1991, p. 209).