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The polyhedron resulting from letting each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces.

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Johnson solid J_4. The bottom eight polyhedron vertices are (+/-1/2(1+sqrt(2)),+/-1/2,0),(+/-1/2,+/-1/2(1+sqrt(2)),0), and the top four polyhedron vertices are ...

There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...

Jessen's orthogonal icosahedron is a concave shaky polyhedron constructed by replacing six pairs of adjacent triangles in an icosahedron (whose edges form a skew ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

The pentagrammic antiprism is the uniform polyhedron with Maeder index 79 (Maeder 1997), Coxeter index 34 (Coxeter et al. 1954), and Har'El index 4 (Har'El 1993). It will be ...

The pentagrammic crossed antiprism is the uniform polyhedron with Maeder index 80 (Maeder 1997), Coxeter index 35 (Coxeter et al. 1954), and Har'El index 5 (Har'El 1993). It ...

The pentagrammic prism is the self-intersecting uniform polyhedron with Maeder index 78 (Maeder 1997), Coxeter index 33 (Coxeter et al. 1954), and Har'El index 3 (Har'El ...

A flexible polyhedron due to C. Schwabe (with the appearance of having four horns) which flexes from one totally flat configuration to another, passing through intermediate ...