IV16 Flattening: relation between dihedral and plane angles ............................................... 162
17 Paper surfaces .............................................................................................................. 1 65
Real and virtual
A conoid of paper ........................................................................................................ 169
A twisted column (salomonic) ..................................................................................... 170
18 Polyhedra ..................................................................................................................... 174
18.1 A kneading-trough ....................................................................................................... 175
18.2 Pyramids ...................................................................................................................... 179
18.2.1 Triangular pyramids..................................................................................................... 1 79
Tetrahedral. With tri-rightangled vertex.
18.2.2 Quadrangular pyramids................................................................................................ 180
Virtual. Triangle-equilateral.
18.2.3 Pentagonal pyramid ..................................................................................................... 18 2
18.2.4 Hexagonal pyramid ...................................................................................................... 18 3
18.2.5 Rhombic pyramid ........................................................................................................ 18 4
18.3 Prisms .......................................................................................................................... 185
18.4 Truncated prism ........................................................................................................... 1 85
18.5 Prism torsion: Obtention of prismoids......................................................................... 185
Triangled, quadrangled and pentagonal
18.6 Regular polyhedra ........................................................................................................ 19 1
Relations within: dodecahedron, icosahedron and stellate penta-
gon.
18.7 Tetrahedron .................................................................................................................. 196
Pyramidal. Wound up. Bi-truncated. Ex-triangle. Skeletonlike
18.8 Cube ............................................................................................................................. 197
Ex-rectangle. Cube of the sum of two numbers. Magic cube (Jer-
emy Shafer). With half (or double) volume. Laminar. Diophantine
cubes.
18.9 Octahedron................................................................................................................... 206
Bipyramidal. Wound up. Ex-tetrahedron. Made of two interlocked
domes. Skeletonlike.
18.10 Perforated pentagonal-dodecahedron........................................................................... 208