## Platonic & Archimedean SolidsWhereas Sacred Geometry introduced readers to two-dimensional forms, Platonic & Archimedean Solids presents the world of three dimensions, which was understood as early as neolithic time. Daud Sutton elegantly explores the eighteen forms-from the cube to the octahedron and icosidodecahedron-that are the universal building blocks of three-dimensional space, and shows the fascinating relationships between them. For anyone interested in design, architecture, and mathematics, this will be a delight. |

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### Contents

Introduction | 1 |

A Short Proof | 14 |

The Kepler Polyhedra | 28 |

Four Explosions | 42 |

Expansions and Formulas | 55 |

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### Common terms and phrases

12 edges 2-fold face 3-fold from vertex 30 edges ARCHIMEDEAN DUALS axes passing axial diagonals beautiful forms bottom left bottom right circumradius circumsphere compound of ﬁve compound polyhedra cube’s cuboctahedron dihedral dodecahedron has twelve Dual pairs edge length edge midpoints equal equilateral triangles face centers ﬁrst ﬁve cubes ﬁve Platonic solids geodesic give the compound golden ratio half turn hedron Icos icosahedral symmetry icosidodecahedron identical vertices illustrated opposite inradius insphere interior diagonals ISBN jitterbug Joining Kepler known laevo lesser circles midsphere mirror planes octagonal octahedra octahedral symmetry pentagram PLATONIC &ARCHIMEDEAN SOLIDS polyhedra shown polyhedron Polytopes radial projection rectangle regular polygon regular solids rhombic dodecahedron rhombicosidodecahedron rhombicuboctahedron snub cube snub dodecahedron solid angle sphere spherical square faces structure tesseract thirteen Archimedean solids top right triangular atom triangular faces truncated cube truncated dodecahedron truncated icosahedron truncated octahedron truncated solids truncated tetrahedron twelve pentagonal twenty type of face