Welcome to the
GEOMETRY GARRET!

A Pot-Pourri of People, Pictures, Places, Penrose Patterns, Polyhedra, Polyominoes, Posters, Posies, and Puzzles

Alan H. Schoen
schoenah@gmail.com

Comments are welcome!

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OUTLINE OF TOPICS

• A. Polyhedra

  • 1. Roundest Polyhedra
    

• B. Finite tilings by rhombs

  • 1. Rosettes and pseudo-rosettes
    

  • 2. Rombix

    KADON'S versions of ROMBIX

• C. Infinite tilings by rhombs

  • 1. Penrose tilings and pseudo-Penrose tilings
    

  • 2. d7-symmetric generalized Penrose tilings derived from de Bruijn heptagrids
    

  • 3. RPn tilings (recursive pseudo-Penrose tilings of dn symmetry)
    

  • 4. Rhombic wallpaper (periodic tilings derived from a variant form of the de Bruijn multigrid)

• D. K-patterns: images derived from partial sums of power and polynomial residues
  

• E. Triply Periodic Minimal Surfaces (TPMS)

  • 0. Mathematical Preliminaries
    
    
  • 1. The P-G-D surface family
    
    

  • 2. Cubic lattice surfaces not in the P-G-D family
    
    

  • 3. Triangle lattice surfaces
    

  • 4. Surfaces on other lattices
    

  • 5. Background

  • 6. Bibliography

  • 7. Minimal surface people
    
    

• F. Other mathematicians and physicists
  
  

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FUTURE STUFF

• 2-dimensional puzzles

  • QUARKS
    

  • LOMINOES (for an illustrated eleven-page description of LOMINOES, look here)
    

• 3-dimensional puzzles
  • TETRONS, CUBONS, OCTONS, DODECONS, and ICONS
    

  • INCUBUS cube puzzle

  • OCTO (double set of the eight solid tetrominoes)
    

  • STARBIX and other closed chains of polyhedra
    

• posters
  • RHOMBBURST
  • H, a minimal surface parametrized by Hermann Amandus Schwarz in 1866
  • F-RD, a minimal surface identified by the author in 1969