Polyabolo 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-triabolo can form a P-triabolo at double scale, or four times as large:

Reptiles are known for polyominoes, polyiamonds, polyaboloes, 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 polyaboloes.

Number of
Cells
Number of
Reptiles
Number of
Bireptiles
111
233
313
4510
503
6719
704

Triaboloes

Tetraboloes

Pentaboloes

Hexaboloes

Heptaboloes

Last revised 2015-12-10.


Back to Bireptiles < Polyform Tiling < Polyform Curiosities
Col. George Sicherman { HOME | MAIL }