Table Of ContentOrigami Polyhedra Design
Origami Polyhedra Design
John Montroll
A K Peters, Ltd.
Natick, Massachusetts
CRC Press
Taylor & Francis Group
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Version Date: 20150225
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To Himanshu
Contents
Symbols xi
Basic Folds xii
Introduction xiii
Part I: Designing Origami Polyhedra 1
Polyhedra Overview 3
Design Factors and Techniques 7
Math and Design 19
Design Method Examples 39
Polygons 45
Equilateral Triangle ✩ 46
Pentagon ✩ 48
Hexagon ✩ 52
Heptagon ✩ 54
Octagon ✩ 56
Silver Rectangle ✩ 57
Bronze Rectangle ✩ 58
Golden Rectangle ✩ 59
Part II: Platonic and Related Polyhedra 61
Tetrahedron Design 63
Tetrahedron ✩ 65
Duo-Colored Tetrahedron ✩✩ 67
Striped Tetrahedron ✩✩ 69
Tetrahedron of Triangles ✩✩ 72
Stellated Tetrahedron ✩✩ 76
Dimpled Truncated Tetrahedron ✩✩✩ 79
Cube Design 83
Cube ✩✩ 87
Striped Cube ✩✩ 89
Triangles on Cube ✩✩ 92
Cube with Squares ✩✩ 95
Stellated Octahedron ✩✩ 98
Cubehemioctahedron ✩✩✩ 100
Dimpled Rhombicuboctahedron ✩✩✩ 104
Stacked Cubes ✩✩✩✩ 108
Simple ✩
Intermediate ✩✩
Complex ✩✩✩
Very Complex ✩✩✩✩
Octahedron Design 113
Octahedron ✩✩ 115
Striped Octahedron ✩✩ 118
Duo-Colored Octahedron ✩✩ 121
Stellated Cube ✩✩ 124
Octahemioctahedron ✩✩✩ 127
Dimpled Truncated Octahedron ✩✩✩ 131
More Platonic Solids Design 135
Icosahedron ✩✩✩ 137
Dodecahedron ✩✩✩✩ 140
Sunken Platonic Solids Design 147
Sunken Octahedron ✩✩ 150
Sunken Tetrahedron ✩✩✩ 153
Sunken Cube ✩✩✩ 157
Sunken Dodecahedron ✩✩✩✩ 161
Sunken Icosahedron ✩✩✩✩ 166
Part III: Dipyramids and Dimpled Dipyramids 171
Dipyramid Design 173
Triangular Dipyramid 90° ✩ 178
Triangular Dipyramid ✩✩ 180
Triangular Dipyramid in a Sphere ✩✩ 183
Tall Triangular Dipyramid ✩✩ 186
Tall Square Dipyramid ✩✩ 189
Silver Square Dipyramid ✩✩ 192
Squat Silver Square Diamond ✩✩ 194
Pentagonal Dipyramid ✩✩ 197
Pentagonal Dipyramid 45° ✩✩ 201
Pentagonal Dipyramid in a Sphere ✩✩ 203
Golden Pentagonal Dipyramid ✩✩ 206
Squat Golden Pentagonal Dipyramid ✩✩ 208
Hexagonal Dipyramid ✩✩ 210
Silver Hexagonal Dipyramid ✩✩ 213
Hexagonal Dipyramid 36° ✩✩ 214
Hexagonal Dipyramid in a Sphere ✩✩ 215
Squat Silver Hexagonal Dipyramid ✩✩ 218
Heptagonal Dipyramid ✩✩✩ 219
Heptagonal Dipyramid 30° ✩✩✩ 223
Heptagonal Dipyramid in a Sphere ✩✩✩ 225
Octagonal Dipyramid ✩✩✩ 229
Octagonal Dipyramid 26° ✩✩✩ 232
Octagonal Dipyramid in a Sphere ✩✩✩ 234
Nonagonal Dipyramid ✩✩✩ 237
Decagonal Dipyramid ✩✩✩ 240
viii Contents
Dimpled Dipyramid Design 243
Tall Dimpled Square Dipyramid ✩✩ 247
Dimpled Silver Sqare Dipyramid ✩✩✩ 250
Heptahedron ✩✩✩ 254
Dimpled Squat Square Dipyramid ✩✩✩ 258
Tall Dimpled Hexagonal Dipyramid ✩✩✩✩ 262
Dimpled Silver Hexagonal Dipyramid ✩✩✩✩ 267
Dimpled Hexagonal Dypyramid ✩✩✩✩ 270
Dimpled Hexagonal Dipyramid in a Sphere ✩✩✩✩ 275
Octagonal Flying Saucer ✩✩ 280
Dimpled Octagonal Dipyramid in a Sphere ✩✩✩ 283
Dimpled Octagonal Dipyramid ✩✩✩ 287
Dimpled Silver Octagonal Dipyramid ✩✩✩ 288
Contents ix
