Zome Geometry : Hands on Learning With Zome Models

Introduction ix Angles, Polygons, Polyhedra Teacher Notes 1(2) Angles and Regular Polygons 3(1) Prisms, Antiprisms, and Pyramids 4(2) Zome System Components, Notation, and Scaling 6(5) Explorations 1 8(1) Icosahedron and Dodecahedron Teacher Notes 9(2) Building and Counting 11(1) Scaling 12(6) Explorations 2 13(2) The Platonic Solids Teacher Notes 15(3) Green Polygons 18(1) The Regular Tetrahedron and Octahedron 19(2) Only Five Platonic Solids: A Proof 21(1) Truncation 22(4) Exploration 3 23(2) Counting Strategies Teacher Notes 25(1) Counting Strategies 26(4) Explorations 4 28(1) Symmetry Teacher Notes 29(1) Icosahedron and Dodecahedron Symmetries 30(2) Simple Polyhedra Symmetries 32(2) Cube and Related Symmetries 34(5) Explorations 5 35(2) Euler's Theorem Teacher Notes 37(2) Faces, Vertices, and Edges 39(2) Topology 41(6) Explorations 6 43(2) Sum and Ratio Patterns Teacher Notes 45(2) Finding the Patterns Using Geometry 47(2) Finding the Patterns Using Measurement 49(2) The Golden Ratio and Scaling 51(6) Explorations 7 53(2) Tessellations Teacher Notes 55(2) Basic Tessellations 57(2) Nonperiodic Tilings 59(6) Explorations 8 60(3) Duality Teacher Notes 63(2) Dual Tessellations 65(1) Dual Platonic Solids 66(1) Dual Polyhedra 67(6) Explorations 9 69(2) Descartes' Theorem Teacher Notes 71(2) Angular Deficit 73(3) Nonconvex Polyhedra 76(4) Explorations 10 78(1) Cubes in a Dodecahedron Teacher Notes 79(1) One Cube 80(1) Five Cubes 81(1) Related Constructions 82(11) Explorations 11 83(4) The Archimedean Solids Teacher Notes 87(6) The Icosidodecahedron 93(1) Archimedean Solids and Notation 94(1) Archimedean Solids in the Zome System 95(6) Explorations 12 97(2) Zome Lengths and Angles Teacher Notes 99(2) Lengths 101(3) Angles 104(2) Dihedral Angles 106(4) Explorations 13 108(1) Zonohedra Teacher Notes 109(1) Rhombic Zonohedra 110(2) Zones 112(2) Stars 114(6) Explorations 14 116(3) Area Teacher Notes 119(1) Calculating Area 120(1) Scaling Area 121(4) Explorations 15 122(1) Space Structures Teacher Notes 123(2) Filling Space 125(3) Packing Spheres 128(2) The FCC Lattice 130(6) Explorations 16 132(3) Volume Teacher Notes 135(1) Prisms and Scaling 136(1) Pyramids and Beyond 137(5) Explorations 17 138(1) Big Domes Teacher Notes 139(2) Guidelines for Building Big Domes 141(1) Zonish Big Domes 142(2) Single-Layer Domes 144(2) Two-Layer Domes 146(5) Explorations 18 147(2) Coordinates Teacher Notes 149(2) Vertex Coordinates 151(2) Point Operations 153(8) Explorations 19 156(3) Self-Intersecting Polyhedra Teacher Notes 159(2) Self-Intersecting Polygons 161(2) The Kepler-Poinsot Polyhedra 163(3) Uniform Polyhedra 166(9) Explorations 20 169(4) The Fourth Dimension Teacher Notes 173(2) Hypercubes 175(3) Simplexes 178(1) Coordinates and Cross Polytopes 179(1) The 120-Cell 180(4) Explorations 21 182(1) Stellations Teacher Notes 183(1) Stellated Polyhedra 184(2) More Stellations 186(6) Explorations 22 188(3) Fractals Teacher Notes 191(1) Introduction to Fractals 192(2) Sierpinski in Three Dimensions 194(2) More Three-Dimensional Fractals 196(4) Explorations 23 198(1) Proofs of Euler's and Descartes' Theorems Teacher Notes 199(1) Proof of Euler's Theorem 200(3) Proof of Descartes' Theorem 203(2) Explorations 24 204(1) Further Explorations 205(8) Answers 213(44) Resources 257(2) Index of Polyhedra 259(6) Zome Struts 265