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Après Kepler ... Sir Roger Penrose

Caspar & Fontano        Kepler's tiling with pentagons and decagons and a P = 34 pentiling generated from Kepler's matrix.

Sarah, Juli and Mark      Penrose Tiling quilt.

Lisbeth G Clemens   This quilt was designed and crafted  in the summer, 1993

Ivars Peterson    Clusters and Decagons,  New rules for constructing a quasicrystal

Pentaplex   the home of seriously perplexing products

Kadon Enterprises   Investigating the strange phenomena of five-fold symmetry.

Karen Wiedman / Rashomond   Penrose Tilings and the Golden Mean

Quasitiler    QuasiTiler draws Penrose tilings and their generalizations. This document explains the interesting geometry involved in the processes.
The concepts involved are surprisingly simple. The only apparent hurdle that we have to overcome is working in spaces with more than 3 dimensions.
However in the next section we start with examples in 2 and 3 dimensions where our intuition is useful. Then we extend the same concepts to more dimensions.

Steffen Weber   This page is meant to be a short introduction to the field of Quasicrystals in order to educate the interested reader on some basic concepts in this
relatively new branch of Crystallography. The more advanced reader may proceed to other sites and sources on quasicrystals.
This page is intended for those having no prior knowledge in this field.

Ron Lifshitz.   Condensed Matter Physics.  California Institute of Technology.   The Symmetry of Quasicrystals.

E. Arthur Robinson, Jr.   Research related pictures
Here is a a picture of a Penrose tiling colored to indicate the presence of a Z^2 section.

Miami University. History of the Penrose Tiling - Bachelor Hall    The tiling was installed in 1979 and is believed to be the first Penrose tiling
incorporated in the design of a public building.

Fractint L-System Tilings,  A tutorial by William McWorter

HAADF  Image          "Structural Study of Al72Ni20Co8 Decagonal Quasicrystal by High-angle Annular Dark-field Image method"
by K. Saitoh, K. Tsuda, M. Tanaka and A. P. Tsai,
Japanese Journal of Applied Physics, Vol.36 (1997) L1400 - L1402.

Brian Hayes     Digital Diffraction

David E. Joyce  :  Hyperbolic Tessellations

 The Association of Teachers of Mathematics        Practical resources, Extensively used from infant to post 16

 Ron Knott   Fascinating Flat Facts about Phi
On this page we meet some of the marvellous flat (that is, two dimensional) geometry facts related to the golden section number Phi.

 The Geometry Junkyard: Penrose Tiling