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The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

The snub cube, also called the cubus simus (Kepler 1619, Weissbach and Martini 2002) or snub cuboctahedron, is an Archimedean solid having 38 faces (32 triangular and 6 ...

The truncated octahedron is the 14-faced Archimedean solid with faces 8{6}+6{4}. It is also the uniform polyhedron with Maeder index 8 (Maeder 1997), Wenninger index 7 ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

If q is logically deducible from p, this is written p|-q.

A divergent sequence is a sequence that is not convergent.

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...