- Preface
- I. User Guide
- II. Mathematics Background
- 7. Case Studies
- Tetrahedron Stellation I (Deltoid)
- Truncated Deltoid
- Tetrahedron Iterated Stellation 3_1
- Tetrahedron Stellation II
- Tetrahedron Reticulated
- Tetrahedron Reticulated (big)
- Tetrahedron Reticulated (tall)
- Tetrahedron Reticulated (huge)
- Octahedron stellation II
- Icosahedron
- Icosahedron Stellation I
- Icosahedron Stellation II
- Cube Triang II
- Yabi
- Bipyramid Octa
- L2(7)
- M(24)
- Torus 3x4
- Trapezohedron
- S(5)
- A(6)
- Quad Star
- Reticulated 2x2 Cube
- Reticulated 3x3 Cube Variants
- Rhombic Dodecahedron
- Zonotope 5
- Monkgau
- Costa-Hoffman minimal surface
- Quad Hex tesselation on a torus
- Pentagonal Quasicrystals
- Heptagonal Quasicrystals
- DoubleDodecahedron
- Icositetra
- Dode Tor 6
- Torus Hexa 3x5
- Hexa Tor
- Hexa UnOrient
- Fancy Heptas
- ToDo

- 8. Graphs and Combinatorics
- 9. Algebraic, Difference and Geometric Topology
- 10. Knots and Links
- 11. Group Theory
- 12. Representation Theory
- 13. Lie Groups and Algebras
- 14. Algebra
- 15. Lattices
- 16. Geometry
- 17. Mathematical Physics
- 18. Chess Pieces Groups
- 19. Complexity Theory
- 20. Resume

- III. Appendix

**List of Figures**

- 2.1. 3D Texture example
- 3.1. The Overall Architecture
- 3.2. New Game
- 3.3. Chess Piece Type C
- 3.4. Chess Piece Type F
- 3.5. After a Checkmate
- 3.6. Go on Hexa Tor
- 3.7. Ko on a boundary
- 3.8. 2-stage Ko 0
- 3.9. 2-stage Ko I
- 3.10. 2-stage Ko II
- 3.11. 2-stage Ko III
- 3.12. 2-stage Ko IV
- 3.13. 2-stage Ko V
- 3.14. Go 3 players
- 3.15. Random Go
- 3.16. Load Game
- 3.17. Client Mirror View
- 3.18. XiStrat Client in Applet Mode
- 7.1. Stellated Tetrahedron
- 7.2. Truncated Deltoid
- 7.3. Tetrahedron Stellation I(iterated)
- 7.4. Tetrahedron Stellation II
- 7.5. Tetrahedron Reticulated 0
- 7.6. Tetrahedron Reticulated I
- 7.7. Tetrahedron Reticulated II
- 7.8. Tetrahedron Reticulated III
- 7.9. Octahedron stellation II
- 7.10. Icosahedron
- 7.11. Icosahedron Variant 1
- 7.12. Icosahedron Stellation I
- 7.13. Icosahedron Stellation II
- 7.14. Cube Triang II
- 7.15. Yabi
- 7.16. Bipyramid Octa
- 7.17. L2(7) Regular
- 7.18. M(24)
- 7.19. Torus 3x4
- 7.20. Trapezohedron
- 7.21. S(5)
- 7.22. A(6)
- 7.23. Quad Star
- 7.24. Cube 2x2
- 7.25. Cube 3x3
- 7.26. 3x3 rotated corner
- 7.27. 3x3 rotated 2x2
- 7.28. 3x3 rotated 3x3 area
- 7.29. 3x3 follow up
- 7.30. Rhombic Dodecahedron
- 7.31. Zonotope 5
- 7.32. Monkgau
- 7.33. Costa-Hoffman
- 7.34. Quad Hex
- 7.35. Pentagonal Quasicrystal 0
- 7.36. Pentagonal Quasicrystal I
- 7.37. Pentagonal Quasicrystal II
- 7.38. Pentagonal Quasicrystal III
- 7.39. Pentagonal Quasicrystal IV
- 7.40. Heptagonal Quasicrystal 0
- 7.41. DoubleDodecahedron
- 7.42. Icositetra
- 7.43. Dode Tor 6
- 7.44. Torus Hexa 3x5
- 7.45. Hexa Tor
- 7.46. Hexa UnOrient
- 7.47. Fancy Heptas
- 10.1. KnotViewer Trefoil
- 10.2. Dode Tor 6 knot
- 10.3. Borromean rings
- 10.4. Dode Tor 6 Link
- 10.5. Hexa Tor Knot
- 11.1. Holonomy
- 15.1. Penrose Quasicrystal in Progress

**List of Tables**

- 3.1. Piece Moving Rules
- 8.1. Polyhedra Cycle Index
- 11.1. Holonomy Groups
- 11.2. c and rot as words
- 11.3. Relations of (Binary) Polyhedral Groups
- 11.4. Schur multiplier
- 11.5. Holonomy Group Schur Covers
- 11.6. Cross Groups on Polyhedra
- 11.7. Galois Groups
- 18.1. 2-Body Groups
- B.1. Hardware
- B.2. Software

**List of Examples**

**List of Equations**

- 8.1. Polyhedra Cycle Index
- 9.1. Euler formula
- 9.2. Euler Characteristic and Betti Numbers
- 11.1. Riemann-Hurwitz identity
- 11.2. Frobenius formula
- 11.3. Short Sequence
- 11.4. Commutative Diagram
- 11.5. A(4) Short Exact Sequence
- 13.1. Baker-Campbell-Hausdorff formula
- 14.1. Hilbert's Nullstellensatz
- 15.1. Dirichlet Series Generating Function F
_{2} - 17.1. Simple Dynamical 2-Body System