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A convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities mx<=b, where m is a real s×3 matrix and b is a real s-vector. ...

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

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

The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

The augmented dodecahedron is Johnson solid J_(58), which is formed from augmentation of one of the faces of the regular dodecahedron by an equilateral pentagonal pyramid. It ...

The augmented hexagonal prism is Johnson solid J_(54), which is formed from augmentation of one of the lateral faces of an equilateral hexagonal prism by an equilateral ...

The augmented pentagonal prism is Johnson solid J_(52), which is formed from augmentation of one of the lateral faces of an equilateral pentagonal prism by an equilateral ...

The augmented sphenocorona is Johnson solid J_(87), which is formed from augmentation of one of the square faces of the sphenocorona by an equilateral square pyramid. The ...