Polyiamond Tetrads

A tetrad is a plane figure made of four congruent shapes, joined so that each shares a boundary with each. Here I show various minimal tetrads for polyiamonds. The smallest polyiamond tetrads use 10-iamonds. According to Karl Scherer, Frank Rubin may have found the first solution. The purple solutions were found by Juris Čerņenoks.

Symmetric Tiles

The smallest tetrad made from a polyiamond with mirror symmetry uses 12-iamonds:

The smallest tetrad made from a polyiamond with birotary symmetry uses 16-iamonds:

The smallest tetrads made from polyiamonds with horizontal mirror symmetry use 17-iamonds:

The smallest tetrad made from a polyiamond with ternary symmetry uses 22-iamonds:

The smallest tetrads made from polyiamonds with ternary symmetry about a vertex use 27-iamonds:

Restricted Motion

The smallest polyiamonds that form tetrads without being reflected are these 10-iamonds:

They are also the smallest polyiamonds that form tetrads without being rotated 60° or 180°.

Holeless

The smallest holeless tetrad made from a polyiamond with mirror symmetry uses 22-iamonds. It was found independently by Robert Ammann, Greg Frederickson, and Jean L. Loyer.

Last revised 2018-11-11.


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Col. George Sicherman [ HOME | MAIL ]