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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 ...

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 ...

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 ...

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, ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

Bayesian analysis is a statistical procedure which endeavors to estimate parameters of an underlying distribution based on the observed distribution. Begin with a "prior ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...