## Three Dimensional Nets and Polyhedra |

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### Contents

Introductory | 3 |

Uniform nets | 12 |

Topological characterization of threedimensional nets | 21 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

3-connected nets 3-connected points 3D 4-connected 3D polyhedron 6-tunnel 8-tunnel unit Acta Crystallogr alternate Archimedean Archimedean solids atoms AX3 structure axis bond angles Catalan Catalan solids closest packing complement complementary polyhedron connected coplanar corresponding crystallographic cubic diamond cubic symmetry derived dodecahedron dual edges equal numbers equivalent example finite form a 3D four framework half-space-filling hedron helices icosahedron identical illustrated in Fig interbond angles interpenetrating nets joined kinds of nonequivalent lattice n-gons nodes nonequivalent link nonequivalent point number of points octahedron plane 6-gon plane nets Platonic solids point symbol poly polygons polyhedron based polyhedron of Fig prisms projection in Fig regular 3D polyhedra regular plane repeat unit represent screw axes shortest circuits shown in Fig simplest snub cubes solutions Space group sphere packing stereo-pair in Fig structure based surface symmetrical configuration tessellation tetragonal tetrahedra triangles truncated octahedra truncated tetrahedra tunnels uniform nets unit cell values vertex vertices