Polyzoid Symmetry Spectra

All images Abaroth 2016. Permission is given to reproduce for non-profit purposes only.

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Patterns created from copies of a single piece which exhibit the highest possible symmetries. The first column contains the Baiocchi figures with maximal symmetry, and the last has the patterns which have no overall symmetry. In each case the example shown has the fewest pieces so that the pattern displays no higher symmetries. Note that some patterns are only possible in the extended grid, and others break the grid completely. Patterns marked * courtesy of George Sicherman.

 

Monozoid

Full 12-Rotary Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Tetrarotary Double Bilateral
* *

 

Dizoids & Extended Dizoids

 

Full 12-Rotary Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Tetrarotary Double Bilateral
X X *
*
X X X X X X
*
* * * * * *
* * * * * *
* * * * * *
* * * * *
X * X * * X

Trizoids

Full 12-Rotary Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Tetrarotary Double Bilateral
*
X X X
X X X
X X X
*
* * *
* *
* *
X X X
X X X

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