******* Introduction *******

These regular polyhedra were produced on Maple, which contains an extensive library of polyhedra, including many less symmetrical examples.

Certain star-polyhedra are better conceived on the screen with `hidden lines' masked. This is tricky to implement properly. In particular, the great icosahedron does not seem quite right.

Regular Polyhedra The regular tetrahedron {3,3}.

Regular Polyhedra The regular hexahedron: O.K. the cube {4,3}.

Regular Polyhedra The regular octahedron {3,4}.

Regular Polyhedra The regular dodecahedron {5,3}.

Regular Polyhedra The regular icosahedron {3,5}.

Regular Polyhedra The great dodecahedron {5,5/2}.

Regular Polyhedra The small stellated dodecahedron {5/2,5}.

Regular Polyhedra The great icosahedron {3,5/2}.

Regular Polyhedra The great stellated dodecahedron {5/2,3}.

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All the convex regular polyhedra press here.

The Kepler-Poinsot star-polyhedra press here.

Two dual Petrie-Coxeter polyhedra press here.

The remaining (self-dual) Petrie-Coxeter polyhedron press here.

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Here we observe how the mirrors for the reflection groups in 3-space subdivide a sphere into right spherical triangles. In other words, this represents the Coxeter complex for certain finite Coxeter groups of rank 3.

The groups [3,3] (tetrahedral symmetry), [3,4] (octahedral symmetry) and [3,5] (icosahedral symmetry) here.

Try viewing the next few in `landscape mode' - computers are irritating!

The group [2,3] (dihedral symmetry) here.

The group [2,4] (dihedral symmetry) here.

The group [2,5] (dihedral symmetry) here.

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Problems to Help you Learn about Isometries

Problems on Euclidean d-space, its isometries and regular polygons press here.

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How might we sensibly define abstract polytopes in real Euclidean space? press here.

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