On Pythagorean Pyramid we tried to build a tetrahedron out of four equal right angled triangles, but the attempt fell flat (pun intended!).

Is it possible to have a tetrahedron built out of right angled triangles, dropping the condition that all triangles be the same? Can you manage to have three equal faces? Or maybe two pairs of equal faces?

I don't know if such a tetrahedron is possible, but if three faces are the same then the fourht must also be equal to them.

If we have three p-q-r triangles, as each side is shared by two adjacent faces, we would need another p-q-r triangle in order to have even quantities of p's, q's and r's. The only solution is that the fourth face must also be a p-q-r triangle.

Thus, we cannot have three equal faces and a different one.

Posted by e.g. on 2004-05-03 14:09:55