Tiling a Polytan With Unequal Monotans

A polytan or polyabolo is a plane figure formed by joining equal isosceles right triangles along equal edges. Every polytan can be dissected into monotans scaled at all different sizes. Dissections into unequal similar pieces are sometimes called perfect.

Here I show some minimal known dissections for polytans with up to five cells, omitting polytans that can be obtained by enlarging smaller polytans.

Ditans

7
7

Tritans

13
2
2
2

Tetratans

8
8
8
8
8
8
8
8
7
8
15

Pentatans

13
8
11
13
11
11
8
2
8
11
8
19
14
8
8
14
13
8
8
8
14
8
8
2
8
2
18
14
2
2

Last revised 2019-08-29.

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Col. George Sicherman [ HOME | MAIL ]