Polydrafter Bireptiles

Introduction

In combinatorial geometry a reptile is a geometric figure, equal copies of which can be joined to form an enlarged form of the figure. For example, four copies of the P-hexiamond can form a P-hexiamond at double scale, or four times as large:

Reptiles are known for polyominoes, polyiamonds, polyaboloes, polydrafters, and other polyforms.

Few polyforms of any kind form reptiles. A bireptile is a figure of which copies can be joined to form two joined, equally enlarged copies of the original figure.

Any figure with a reptiling trivially has a bireptiling, but not every figure with a bireptiling has a reptiling. That is, bireptiles are more common than reptiles.

Below I show minimal known bireptilings for various polydrafters.

Number of
Cells
Number of
Reptiles
Number of
Bireptiles
111
255
329
4922

Didrafters

Tridrafters

Tetradrafters

Last revised 2015-12-11.


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Col. George Sicherman { HOME | MAIL }