Tetrabolos – the puzzle pieces

The 14 Tetrabolos each consist of four congruent isosceles right triangles. Within each Tetrabolo, the triangles are joined either along their hypotenuses or along their legs; a hypotenuse never meets a leg.

Tetrabolos belong to the polyabolo family, also known as polytans.

All 14 Tetrabolo pieces

Tetrabolo Puzzles

Martin Gardner describes the Tetrabolos in his book Mathematical Magic Show. Together, the 14 Tetrabolos cover an area of 56 isosceles right triangles.

The underlying grid allows figures with up to fourfold rotational symmetry and four axes of reflection. However, no figure with this maximum symmetry can be assembled from all 14 Tetrabolos. The rectangle shown also cannot be assembled from all 14 pieces. The few known symmetric figures made from all 14 pieces have at most one axis of reflection.

Examples of Tetrabolo Figures

Rectangle figure made from 14 Tetrabolos
Rectangle with no solution
Figure made from 14 Tetrabolos
Figure made from 14 Tetrabolos
Cross figure made from 12 Tetrabolos
Fully symmetric figure made from 12 Tetrabolos
Figure made from 13 Tetrabolos
Fully symmetric figure made from 13 Tetrabolos
Tetrabolo figure 02
14 Tetrabolos – 925 solutions
Tetrabolo figure 01
14 Tetrabolos – 747 solutions
Tetrabolo figure 03
14 Tetrabolos – 1777 solutions
Tetrabolo figure 04
14 Tetrabolos – 1075 solutions
Tetrabolo figure 06
14 Tetrabolos – 106 solutions
Tetrabolo figure 07
14 Tetrabolos – 19 solutions
Tetrabolo figure 08
14 Tetrabolos – 863 solutions
Tetrabolo figure 09
14 Tetrabolos – 19 solutions
Tetrabolo figure 14
10 Tetrabolos – 5 solutions
Tetrabolo figure 20
10 Tetrabolos – 27 solutions
Tetrabolo figure 10
9 Tetrabolos – 105 solutions
Tetrabolo figure 11
9 Tetrabolos – 199 solutions

Resources & Downloads

3D-Printing Templates

The 3D-printing files include the 14 Tetrabolos and a box.

3D-printed Tetrabolos
3D-printed Tetrabolo box

Cardboard Templates

The PDF contains templates in several colors and instructions for making a Tetrabolo puzzle from cardboard.

Colorful cardboard templates for Tetrabolos
Magenta cardboard templates for Tetrabolos