1 Contents Preface 1 Zomes, Domes and Clusters 1.1 What Are Zomes? 1.2 What is the Difference Between a Zome and a Geodesic Dome? 2 Zonohedra 2.1 What are Zonohedra? 2.2 Face Planes of Zonohedra 2.3 Section Stars and Face Planes 2.4 Division of Zonohedra into Parallepiped Cells 3 Regular Ways of Arranging Lines in Space 3.1 Three Zones 3.2 Four Zones 3.3 Six Zones 3.4 Ten Zones 4 Clustering 4.1 Twenty-one Zone Structure 4.2 Twenty-one Zone Zome Clusters 5 Stretching a Zone 6 Trusses: Twenty-one Zone System 6.1 6 A Lines 15 C Lines 6.2 Triacontahedron 7 Critical Constants 7.1 Six Zone 7.2 Ten Zone 7.3 Ten Zone 7.4 The Appearance of the CTn Series in the Dimensions of the Triacontahedron and the Enneacontahedron 8 Symmetries of a Regular Thirty-one Zone Star 9 Five-Fold Symmetry 9.1 Growth and Generations of Stars 10 Sections 10.1 R Section 10.2 S Section 10.3 T Section 10.4 V Section 10.5 X Section 10.6 Y Section 10.7 The Formation of Triangles 10.8 A Star Problem 11 The Divine Proportion 11.1 Tau Power Series 11.2 Pattern and Rules 11.3 The Fibonacci Numbers 12 Coherence Proofs 12.1 Two Dimensions 12.1.1 Definition 1 12.1.2 Definition 2 12.1.3 Definition 3 12.1.4 Definition 4 12.1.5 Definition 5 12.1.6 Definition 6 12.2 Three Dimensions 12.2.1 Definition 1 12.2.2 Definition 2 12.2.3 Definition 3 12.2.4 Definition 4 12.2.5 Definition 5 12.2.6 Definition 6 12.2.7 Definition 7 12.2.8 Definition 8 12.2.9 Definition 9 13 Joints 14 The Stars of Other Systems 14.1 Octet Truss 14.2 The Mero Space Grid System 15 Hardware List of Figures List of Tables References Index 2 3