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The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

A one-dimensional line segment where two two-dimensional faces of an n-dimensional polytope meet, also called a side.

There are 10 stellated regular 4-polytopes (Wells 1991, p. 209).

The vertex of a polytope is a point where edges of the polytope meet.

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...

All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center. The theorem was ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

If a cyclic quadrilateral ABCD is inscribed in a circle c_1 of a coaxal system such that one pair AC of connectors touches another circle c_2 of the system at P, then each ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

Pong Hau K'i is an ancient Chinese tic-tac-toe-like game involving two players with two differently colored stones (say, red and blue). The players move their respective ...