Tiling a Rectangle with A Scaled Tetrabolo and a Scaled Pentabolo

Introduction

A tetrabolo or tetratan is a plane figure formed by joining four equal isosceles right triangles at their legs or hypotenuses. A pentabolo or pentatan is a plane figure formed by joining five equal isosceles right triangles at their legs or hypotenuses.

Here are the 14 tetraboloes:

Here are the 30 pentaboloes:

A scaled polyabolo is one that may be used at various scale factors:

Here I show a rectangle tiled by a scaled tetrabolo and a scaled pentabolo, using at least one copy of each and as few total copies as is known to be possible. If you find a solution with fewer tiles or solve an unsolved case, please write.

See also

Tiling a Rectangle with Two Scaled Pentaboloes

Table

  123456789101112131415161718192021222324252627282930
1? ? 26 10 ? 4 ? 18 3 ? ? ? ? 12 10 6 ? ? 24 ? 6 ? ? 6 12 ? 6 ? 4 18
2? ? ? ? ? 24 ? ? 6 ? ? ? ? ? ? ? ? ? ? ? 17 8 ? 20 ? ? ? ? 4 12
316 10 4 14 12 20 20 18 4 20 4 17 8 16 12 12 10 8 10 16 12 28 12 10 22 22 4 22 16 20
4? ? ? ? ? 52 ? ? 5 ? ? ? ? ? ? ? ? ? ? ? 29 ? ? 69 ? ? ? ? 6 32
5? ? ? ? ? 48 ? ? 3 ? 11 ? ? 12 ? ? ? ? ? ? 15 14 ? 10 ? ? ? ? 3 6
6? ? ? 18 12 12 11 ? 3 ? 20 ? 4 12 4 ? 26 ? ? 10 4 12 16 14 22 10 ? 12 8 4
728 28 36 24 28 6 56 10 4 ? 8 24 8 8 15 8 8 56 40 ? 8 8 28 7 8 10 6 ? 6 8
8? ? 17 6 ? 6 ? 13 3 ? ? ? ? 8 8 5 ? ? 16 ? 5 ? ? 5 8 ? 5 ? 6 41
9? ? ? ? ? 60 ? ? 5 ? 48 ? ? 8 ? ? ? ? ? ? 26 ? ? 24 ? ? ? ? 5 12
1044 40 20 18 48 8 48 10 6 76 34 40 18 24 8 8 44 32 24 22 8 14 8 8 20 20 8 17 4 8
11? ? ? ? ? 24 ? ? 3 ? ? ? ? ? 8 8 ? ? ? ? 34 ? ? 82 ? ? 23 ? ? ?
1214 6 12 6 8 6 20 12 4 12 6 6 14 8 8 8 12 10 10 8 8 24 14 9 12 22 6 14 6 11
13? ? ? ? ? 80 ? ? 3 ? 16 ? 17 16 ? ? ? ? ? ? 17 40 ? 10 ? ? ? ? 4 10
146 4 3 4 6 4 6 3 2 6 4 4 3 6 3 4 4 5 3 6 4 4 6 3 6 4 3 4 3 4
  123456789101112131415161718192021222324252627282930

Navigation

Tiles
2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 20
22 23 24 26 28 29 32 34 36
40 41 44 48 52 56 60 69 76
80 82

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Last revised 2025-10-22.

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Col. George Sicherman [ HOME | MAIL ]