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?

(In reply to re(3): Short answer to part 1. by Charlie)

I think I see the problem now.

The corner of a cereal packet (in fact a tea packet, as I've run out of cereal) by definition contains 3 right angled triangles, and is accordingly 'built of right angled triangles'.

If you then cut across one of the edges (I'm not going to define exactly how, as this seems to be causing unnecessary difficulty), you get a tetrahedron with 3 equal right angled sides, which is what was asked for. I've just done exactly that.

Of course, the 4th side is not a right-angled triangle, but the requirement that 'all the triangles be the same' has been 'dropped'.

I wasn't suggesting more than that.

Posted by broll on 2016-03-01 09:30:50