



The Mitre System set and Frames. Patented by Adrian Fisher and Ed Pegg Jr.

Origins



Core Shapes and Supporting Shapes of The Mitre System. Patent Pending by Adrian Fisher and Ed Pegg Jr. For more on the shapes, click here. by Adrian Fisher, Ed Pegg Jr, and Miroslav Vicher

Back in 1998, I (EPJ) noticed the Fisher Pavers over at Adrian's site. I considered these carefully designed heptagons and squares quite clever. They could make some very nice designs, but I didn't find them chaotic enough. So, I started playing with Autocad LT, trying to find something better.



These images of the Fisher Paver System are copyright (c) 2000 by Adrian Fisher. Used with permission.



This image of Ed Pegg's Chaos Tile system is copyright (c) 1998 by Ed Pegg Jr.

1. No fault lines across the tessellation in any direction.

2. Ability to make squares and rectangles.

3. No sharp angles -- they break too easily

4. Under a modular layout, the ability to lay out a design with minimal cutting.

5. Spirals and other curves should be possible by using differently colored bricks.

6. The tiling should be able to interface with the modules of other tiling systems.

7. The tiling should use few pieces.

8. The ability to make both periodic and nonperiodic designs is desirable.

9. The pieces must be of similar size.



Semiregular Dodecagon-Triangle design by Archimedes. Can you find all 8 semiregular tessellations?



n-gon dissections copyright (c) 1998 by Adrian Fisher and Ed Pegg Jr. The 20-gon isn't regular, the others are.



Design C1853 copyright (c) 1998 by Adrian Fisher. Used with permission. 20-piece Square copyright (c) 1998 by Ed Pegg Jr.



Terrazzo Tiling design copyright (c) 1998 by Adrian Fisher. Used with permission.



Nested Squares using the Mitre System copyright (c) 1998 by Ed Pegg Jr.



A variety of squares using the Mitre System copyright (c) 1999 by Ed Pegg Jr, Adrian Fisher, and Miroslav Vicher. Used with permission.



A variety of hexagons using the Mitre System copyright (c) 1999 by Ed Pegg Jr and Adrian Fisher. Used with permission.

I'd gotten to know Miroslav Vicher when he started solving a variety of difficult tiling problems, such as Eternity. After Adrian and I filed the patent, we hired Mira to look for solutions with this system using his program, and he found thousands. Do look at Miroslav Vicher's site, for more. For example, the following is one of over ten thousand dodecagon patterns he found. He found many squares and rectangles that eluded us, and a wide variety of beautiful tessellations.



Dodecagon using the Mitre System copyright (c) 1999 by Miroslav Vicher. Used with permission.

There are more designs by Adrian Fisher available.

For actual paving and house design, this page describes the different scale systems. For all inquiries, please contact:

Adrian Fisher, Victoria Lodge, 5 Victoria Grove, Portsmouth, PO5 1NE, England.

Phone: +44 23 9235 5500 Email: adrian@mazemaker.com



Fountain copyright (c) 2000 by Adrian Fisher. Used with permission.

New Tessellation Systems

But none of the above links gives either of the following tessellations, both done with the same shape. This quadrilateral can tile the plane with either five-fold symmetry or six-fold symmetry.

When I made the Chaos Tiles, I found a large number of interesting tessellations based on the nonagon. Here's one of them.



