Welcome to the
GEOMETRY GARRET!

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

Alan H. Schoen

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, physicists, and chemists
  
  
  

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FUTURE STUFF

• 2-dimensional puzzles

  • QUARKS
    

  • LOMINOES
    
    For an illustrated ten-page introductory booklet about LOMINOES, look here,
    but for an encyclopedic book (131 pages) about LOMINOES, look here.

    NOTE: On pp. 129 and 131 of the LOMINOES book, the address listed as the link to Neil J. A. Sloane's Online Encyclopedia for Integer Sequences
    is obsolete and should be replaced by
    http://oeis.org/
    Be sure to watch (and hear) Tony Noe's spectacular 8.5 minute movie illustrating Sloane's Encyclopedia!

• 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