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A polygon whose vertices do not all lie in a plane.

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

The tridiminished icosahedron is Johnson solid J_(63). Interestingly, its skeleton has the same degree sequence as the triangular cupola.

Johnson solid J_(83).

The space |K| which is the subset of R^n that is the union of the simplices in a simplicial complex K. The term polytope is sometimes used as a synonym for underlying space ...

The uniform polychora are four-dimensional analogs of the uniform polyhedra. In fact, the uniform polyhedra are cells of the uniform polychora. There are more than 8000 known ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge: 1. circle squaring. 2. cube duplication. 3. ...

Miller's rules, originally devised to restrict the number of icosahedron stellations to avoid, for example, the occurrence of models that appear identical but have different ...