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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 ...

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 ...

The placement of objects so that they touch in some specified manner, often inside a container with specified properties. For example, one could consider a sphere packing, ...

The pentagonal prism is a prism having two pentagonal bases and five rectangular sides. It is a heptahedron. The regular right pentagonal prism is uniform polyhedron U_(76). ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...