Polytan 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-tritan can form a P-tritan at double scale, or four times as large:

Reptiles have been found for polyominoes, polyiamonds, polytan, 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 polytans.

Number of
Cells Number of
Reptiles Number of
Bireptiles

1 1 1

2 3 3

3 1 3

4 5 10

5 0 3

6 7 19

7 0 4

Number of Cells	Number of Reptiles	Number of Bireptiles
1	1	1
2	3	3
3	1	3
4	5	10
5	0	3
6	7	19
7	0	4

Tritans

Tetratans

Pentatans

Hexatans

Heptatans

Last revised 2015-12-10.

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Col. George Sicherman { HOME | MAIL }