Polyomino Reptiles

Higher Order Polyominoes

 rep-n for all n > 2

Rep-n for even n is formed from 4x4 or 6x8 rectangles as in the examples below which give solutions for n = 4, 5, 6 and 7.

The diagram below shows an extesion of a rep-(4k+1) to a rep-(4k+5). A similar construction gives an extension of a rep-(4k+3) to a rep-(4k+7).

 rep-n for all n = 12, 16, 20 and others

 rep-n for all n = 32, 36, 40 and others

 rep-n for n = 18k, 21k, 15k (k>2), 24k and others

 rep-n for all n other than 2, 3

Below are solutions for n = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17 and 21

The extension below turns a rep-k to a rep-(k+10) for all k other than 6, 7 and 11 (see possible rectangles).

 rep-n for n = 6, 7, 8, 9, 10, and all n >12

Since a 6x6 square can be made with four copies of this enneiomino it is clear that it is rep-(6k) for all k. The diagrams below show rep-n for n = 7, 8, 9, 10, 16 and 17.

The next diagrams show extensions from

rep-(3n+1) to rep-(3n+7) for n = 2 or n > 4
rep-(3n+2) to rep-(3n+8) for n = 2 or n > 4
rep-(3n+3) to rep-(3n+9) for n > 1