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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 regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

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 ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

To truncate a real number is to discard its noninteger part. Truncation of a (positive) number x therefore corresponds to taking the floor function |_x_|. Truncation also ...

The polyhedron compound of the truncated cube and its dual, the small triakis octahedron. The compound can be constructed from a truncated cube of unit edge length by ...

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

In algebraic topology, a p-skeleton is a simplicial subcomplex of K that is the collection of all simplices of K of dimension at most p, denoted K^((p)). The graph obtained ...