## 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

- 0.
A random polyhedral honeycomb

- 1.
Roundest Polyhedra

B. Finite tilings by rhombs

- 1.
Rosettes and pseudo-rosettes

- 2.
ROMBIX

The three versions of the ROMBIX puzzle available from KADONOf these three

ROMBIXsets, the one young children seem to enjoy most is

the one at the left, which is composed of four sets of ROMBIX-4. It was rediscovered

independently by Kate Jones (founder of KADON), who calls it 'ROMBIX Jr.'The most

versatileof these sets is the one in the middle, the 16-piece ROMBIX-8.

(It's at the bottom of the KADON page, just below ROMBIX Jr.)The most

challengingof these sets is the one at the right, the 36-piece ROMBIX-12 .

My favorite challenge using this set is the following:

1. Choose any one of the six colored subsets of rombiks.

2. Arrange the six rombiks in this subset in a tiling of thecentral ladder.

3. Fill in the rest of the tray with the remaining thirty rombiks to complete acircle tiling.

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 — aka "":resi-doodles

Images derived from partial sums of power and polynomialresidues

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 introductory

bookletabout 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's

Online Encyclopedia for Integer Sequencesis 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,andICONS

INCUBUScube puzzle

OCTO(double set of the eight solid tetrominoes)

STARBIXand other closed chains of polyhedra

- posters

RHOMBBURST(4-color poster), an embedded triply-periodic minimal surface parametrized by Hermann Amandus Schwarz in 1866 (b&w poster)H, an embedded triply-periodic minimal surface identified by the author in 1969 (b&w poster)F-RD