Tetrabolos – The pieces

The 14 tetrabolos each consist of four right isosceles triangles. These triangles touch either along their hypotenuses or along their legs—mixed connections (one hypotenuse and one leg at the same junction) do not occur.

Tetrabolos belong to the family of polyabolos, which are also known as polytans.

Tetrabolo  Puzzle Pieces

Tetrabolo-Puzzles

Martin Gardner introduced the tetrabolos in his book Mathematical Magic Show.
Together, the 14 tetrabolos form an area consisting of 56 right isosceles triangles.

The underlying grid allows shapes with up to fourfold rotational symmetry and four axes of reflection. However, there are no shapes with this maximal symmetry that can be assembled entirely from all 14 tetrabolos. Even the rectangle shown has no solution. The few known symmetrical shapes using all 14 pieces have at most a single axis of reflection.

A selection of Tetrabolo Puzzle shapes
Rectangle shape without solution
Rectangle shape without solution
Shape made from 14 tetrabolos
Shape made from 14 tetrabolos
Shape with maximal symmetrie - 12 Tetrabolos
Shape with maximal symmetrie – 12 Tetrabolos
Shape with maximal symmetrie - 13 Tetrabolos
Shape with maximal symmetrie – 13 Tetrabolos
14 Tetrabolos-925 solutions
14 Tetrabolos-925 solutions
14 Tetrabolos-747 solutions
14 Tetrabolos-747 solutions
14 Tetrabolos-1777 solutions
14 Tetrabolos-1777 solutions
14 Tetrabolos-1075 solutions
14 Tetrabolos-1075 solutions
14 Tetrabolos-106 solutions
14 Tetrabolos-106 solutions
14 Tetrabolos-19 solutions
14 Tetrabolos-19 solutions
14 Tetrabolos-863 solutions
14 Tetrabolos-863 solutions
14 Tetrabolos-19 solutions
14 Tetrabolos-19 solutions
10 Tetrabolos-5 solutions
10 Tetrabolos-5 solutions
10 Tetrabolos-27 solutions
10 Tetrabolos-27 solutions
9 Tetrabolos- 105 solutions
9 Tetrabolos- 105 solutions
9 Tetrabolos-199 solutions
9 Tetrabolos-199 solutions

Resources & Downloads

3D Print Templates

The 3D-print templates consist of 14 Tetrabolo puzzle pieces and a box.

3D printed Tetrabolos
3D printed Tetrabolo Puzzle

Solution program

Tetrabolo Solver Screenshot

The Tetrabolo Puzzle solver is part of a program collection available for download on Itch.io. It is for Windows only.

IMPORTANT: For a correct installation, please read the Instructions before unpacking!


Crafting Templates

Download multi-colored crafting templates and a crafting guide for the cardboard tetrabolo puzzle

Crafting Template
Crafting template