Challenge Level

What is a tetrahedron? Here are four different triangles made from Polydron (plastic shapes which click together):

Small equilateral |
Isosceles |

Right angled isosceles |
Large equilateral |

The sides of the small equilateral triangle are the same length as the short side of the isosceles triangle and the short sides of the right-angled isosceles triangle.

The sides of the large equilateral triangle are the same length as the long sides of the isosceles triangle and the long side of the right-angled isosceles triangle.

You have an unlimited number of each type of triangle.

How many different tetrahedra can you make? Convince us you have found them all.

*Images reproduced with kind permission from Polydron.*