30 Jun
2007
30 Jun
'07
5:07 p.m.
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=BD=B0, distinctly short of the 72=B0 that would let you fit five of th=
em
around a line, but not nearly short enough to fix six of them (60=B0).