A polyhedron is regular if it has as one of its faces just one type of regular polygon, and all its vertices are congruent. There are only five regular polyhedra. Euclid's Elements states " In this book, the thirteenth, are constructed the five figures called Platonic, which however do not belong to Plato. Three of these five figures, the cube, pyramid and dodecahedron, belong to the Pythagoreans, while the octahedron and icosahedron belong to Theætetus."

Euler discovered a relationship between the faces, vertices and edges of these solids: vertices + faces = edges + 2.

JavaView: Help with diagrams
In every diagram you can click and drag the left mouse button to rotate each spae. Press your right mouse button to select different interaction modes from a popup menu, or use keyboard keys to temporarily switch between different modes (just keep a button pressed to switch mode temporarily). Some essential modes are: