29 Jun
2007
29 Jun
'07
9:26 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??, 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?).
Go to a gaming shop and pick up a handful of D4s if you want to fiddle
with regular tetrahedra; it's probably the cheapest and easiest way to
get a bunch of fairly regular tetrahedra in an easily handleable size.
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