A polyhedron is a three-dimensional solid composed of a set of polygons connected at their edges. All of the faces of a polyhedron are flat, as opposed to spheres and cones, which have round surfaces.
Polyhedra can be regular; a regular polyhedron is one composed of regular polygons (polygons where all sides and angles are the same). There are nine regular polyhedra - five convex and five concave. The five convex polyhedra are the cube, tetrahedron, octahedron, dodecahedron, and icosahedron. These five shapes are sometimes referred to as Platonic solids.
Polyhedra composed of two different types of regular polygons are called semiregular polyhedra or Archimedean solids, of which there are thirteen.
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Encyclopedia with virtual reality (VRML) models, history and art of the shapes. Includes background information on each shape, a glossary, guide to names, classroom activities, sculptures by the author, and a bibliography.
Abstract of book about geometric model building.
Biography from an online History of Mathematics, with quotes.
Three dimensional block puzzles, VRML models, instructions for creating real-world shrinkable models, and a gallery of images. In English and Japanese.
Short biography from the University of Toronto.
A set of eight solid aluminum models for purchase, available in several colors.
Images and VRML models of the shapes connected together by their faces.
Data files and sample C code for a large number of the shapes.
More than eighty paper model templates, ready to cut out and fold up, available to print out or download.
List of links to sites on the topic, plus a few renderings of the shapes.
Explains why there can be only five regular polyhedra.
A proof that each configuration of polygons around a vertex results in a unique polyhedron, plus Java applets for rotating the images of the shapes.
The five regular polyhedra mapped onto the surface of their surrounding spheres, which can be rotated in java applets. Also includes a discussion of the mathematical properties of the shapes.
Images of paper models, plus some vrml models. In English, German, and French.
An online encyclopedia of the shapes, including ray-traces and other data on the Platonic Solids, Kepler-Poinsot Polyhedra, and Archimedean Solids.
Puzzle designer's guidebook with designs, plans, and instructions for building geometric dissection puzzles of polyhedra and burrs.
Provides animations and video clips of convex polyhedra, non convex polyhedra, other polyhedra and related subjects. In French and English.
Background information and images of the 59 possible stellated icosahedra.
Discussion of deltahedra, infinite and flexible polyhedra, with images, a java applet, and links.
An article by Jorge Rezende, Lisbon. Includes a deltoidal icositetrahedron, rhombicuboctahedron and rhombic dodecahedron exercise.
[PDF]
Excerpt of Chapter 9 of R. Maeder's book The Mathematica Programmer II. Includes images and statistics for 80 uniform polyhedra, plus background information on the shapes and the wythoff symbol.
Collection of information on polyhedra with images, VRML files, interactive java applets and original research.
Encyclopedia with virtual reality (VRML) models, history and art of the shapes. Includes background information on each shape, a glossary, guide to names, classroom activities, sculptures by the author, and a bibliography.
Biography from an online History of Mathematics, with quotes.
More than eighty paper model templates, ready to cut out and fold up, available to print out or download.
Explains why there can be only five regular polyhedra.
Provides animations and video clips of convex polyhedra, non convex polyhedra, other polyhedra and related subjects. In French and English.
An article by Jorge Rezende, Lisbon. Includes a deltoidal icositetrahedron, rhombicuboctahedron and rhombic dodecahedron exercise.
[PDF]
Collection of information on polyhedra with images, VRML files, interactive java applets and original research.
Abstract of book about geometric model building.
Three dimensional block puzzles, VRML models, instructions for creating real-world shrinkable models, and a gallery of images. In English and Japanese.
Discussion of deltahedra, infinite and flexible polyhedra, with images, a java applet, and links.
An online encyclopedia of the shapes, including ray-traces and other data on the Platonic Solids, Kepler-Poinsot Polyhedra, and Archimedean Solids.
Background information and images of the 59 possible stellated icosahedra.
List of links to sites on the topic, plus a few renderings of the shapes.
Images of paper models, plus some vrml models. In English, German, and French.
Excerpt of Chapter 9 of R. Maeder's book The Mathematica Programmer II. Includes images and statistics for 80 uniform polyhedra, plus background information on the shapes and the wythoff symbol.
Puzzle designer's guidebook with designs, plans, and instructions for building geometric dissection puzzles of polyhedra and burrs.
Short biography from the University of Toronto.
Images and VRML models of the shapes connected together by their faces.
A proof that each configuration of polygons around a vertex results in a unique polyhedron, plus Java applets for rotating the images of the shapes.
The five regular polyhedra mapped onto the surface of their surrounding spheres, which can be rotated in java applets. Also includes a discussion of the mathematical properties of the shapes.
A set of eight solid aluminum models for purchase, available in several colors.
Data files and sample C code for a large number of the shapes.
