solid in three dimensions with flat faces
(Redirected from Polyhedra)
Some polyhedra

(Regular polyhedron)

Small stellated dodecahedron
(Regular star)


Great cubicuboctahedron
(Uniform star)

Rhombic triacontahedron
(Uniform dual)

Elongated pentagonal cupola
(Convex regular-faced)

Octagonal prism
(Uniform prism)

Square antiprism
(Uniform antiprism)

A polyhedron (polyhedra or polyhedrons if more than one) is a geometrical shape. It is a 3D shape with flat faces, and straight edges. Each face is a polygon surrounded by edges. Usually it is known by the number of faces, corners, or edges it has.

Most dice are polyhedra.

There are many groups of polyhedra, which can either be only a small set, or can be infinite. Prisms, pyramids, antiprisms, and bipyramids are groups of polyhedra.

A regular polyhedron has faces that are all the same, corners that are all the same, and edges that are all the same. A uniform polyhedron can have one or two kinds of its parts be all the same.

Definition change

Two types of polyhedron are convex and concave. The edge connecting any two points of a convex polyhedron is inside the polyhedron. The line connecting two points of a concave polyhedron may go outside the polyhedron. The Platonic solids are regular convex polyhedra.

Mathematicians do not always agree on what makes a polyhedron. Some may only consider the convex polyhedra, and disregard the ones that are not convex. Some polyhedra are degenerate, meaning that when drawn as real objects, they look flat.

Naming change

Usually, polyhedra are named by the number of faces they have. The first polyhedra are the tetrahedron, which is made of four triangles, pentahedron (five faces, can look like a four-sided pyramid), hexahedron (six faces, a cube if it is regular), heptahedron (seven faces) and octahedron (eight faces). Prisms, pyramids and other shapes can also be named after how many faces they have.

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