29 Jun
2007
29 Jun
'07
10:51 p.m.
der Mouse wrote:
No, I'm not sure I meant a solid icosahedron. I was only thinking as
far as a tetrahedron has equilateral triangles as faces, and so does an
icosahedron.
Peace... Sridhar
I thing it
would probably be interesting to make a computer where the
building blocks would be tetrahedra, and you would bolt them together
in 3D configurations. Can you make an icosahedron out of tetrahedra?
No - at least not assuming you mean a solid regular icosahedron and
regular tetrahedra. The face-to-face angle of a regular tetrahedron is
not a "nice" angle - it's 2*arcsin(.5/sqrt(.75)), or slightly over
70??, distinctly short of the 72? that would let you fit five of them
around a line, but not nearly short enough to fix six of them (60?).