## 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!

OUTLINE OF TOPICS

- A. Polyhedra

- 1.
Roundest Polyhedra

- B. Finite tilings by rhombs

- 1.
Rosettes and pseudo-rosettes

- 2.
Rombix

KADON'S three versions of ROMBIX

The mostversatileof these threeRombixsets is the 16-piece set forn=8,

which is middle one above.

The mostchallengingone of them is the 36-piece set forn=12 (it's the one

at the right above).

The one that very young children seem to enjoy the most is thecomposite

16-piece set, composed of four 4-piece sets forn=4 (it's the one at the left

above).

- C. Infinite tilings by rhombs

- 1.
Penrose tilings and pseudo-Penrose tilings

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

- 3.
RP(recursive pseudo-Penrose tilings ofntilingsdnsymmetry)

- 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.
TheP-G-Dsurface family

- 2.
Cubic lattice surfaces not in theP-G-Dfamily

- 3.
Triangle lattice surfaces

- 4.
Surfaces on other lattices

- 5.
Background

- 6.
Bibliography

- 7.
Minimal surface people

FUTURE STUFF

- 2-dimensional puzzles

- QUARKS

- LOMINOES

For an illustrated ten-page introductorybookletabout LOMINOES, look here,

but for an encyclopedicbook(131 pages) about LOMINOES, look here.

NOTE: On pp. 129 and 131 of the LOMINOESbook, the address listed as the link to Neil J. A. Sloane'sOnline 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is obsolete and should be replaced by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 (4-color poster)
H, an embedded triply-periodic minimal surface parametrized by Hermann Amandus Schwarz in 1866 (b&w poster)F-RD, an embedded triply-periodic minimal surface identified by the author in 1969 (b&w poster)