Polyhedron

A polyhedron (one polyhedron, many polyhedra, or polyhedrons) 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 defined by the number of faces, or edges.

Some polyhedra
Dodecahedron (Regular polyhedron)	Small stellated dodecahedron (Regular star)
Icosidodecahedron (Uniform)	Great cubicuboctahedron (Uniform star)
Rhombic triacontahedron (Uniform dual)	Elongated pentagonal cupola (Convex regular-faced)
Octagonal prism (Uniform prism)	Square antiprism (Uniform antiprism)

Most dice are polyhedra.

Two types of polyhedron are convex and concave. The line 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.

Mathematicians do not agree on what makes a polyhedron. They do agree that there are five Platonic solids, which are regular polyhedra. On a regular polyhedron, all faces are the same and all vertices are the same.

Naming

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 according to how many faces they have.

Other websites

Eric W. Weisstein, Polyhedron at MathWorld.
Making Polyhedra
Polyhedra Pages
Stella: Polyhedron Navigator – Software for exploring polyhedra and printing nets for their physical construction. Includes uniform polyhedra, stellations, compounds, Johnson solids, etc.
The Uniform Polyhedra
Virtual Reality Polyhedra – The Encyclopedia of Polyhedra
- Polyhedra and Pyramids
Paper Models of Polyhedra Many links
Paper Models of Uniform (and other) Polyhedra
Interactive 3D polyhedra in Java Archived 2005-04-03 at the Wayback Machine
World of Polyhedra Archived 2006-04-14 at the Wayback Machine – Comprehensive polyhedra in flash applet, showing vertices and edges (but not shaded faces)
Polyhedra software, die-cast models, and posters
Electronic Geometry Models – Contains a peer reviewed selection of polyhedra with unusual properties
Symmetry, Crystals and Polyhedra Archived 2017-02-24 at the Wayback Machine
uniform solution for uniform polyhedra by Dr. Zvi Har'El Archived 2011-05-20 at the Wayback Machine
Java applet with the use of kaleido Archived 2007-08-18 at the Wayback Machine
Origami Polyhedra – Models made with Modular Origami
Polyhedra Collection – Various virtual and physical polyhedra models

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