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From: Archimedes Plutonium on 14 Mar 2010 03:21
Alright, I confirmed my suspicions that a tetrahedron in 3D is a no-go
as the best tiler
because of obvious inability to form a solid packing with no gaps in
between.

I found this website to show me the densest tetrahedron packing:

--- quoting from wolfram ---
http://demonstrations.wolfram.com/DensestTetrahedraPacking/

The cover article for the 13 August 2009 issue of Nature published a
packing method for tetrahedra with a packing density of 0.782021, a
new record. For complex packings, space is divided into an orderly
arrangement of identical cells. In this packing, each cell has 72
tetrahedra, shown here.
--- end quoting ---

So that is proof that tetrahedron packing in 3D is not going to be the
maximum tiler.

So what is?

Well, I wonder what the figure is called if you split apart a cube or
a rectangular solid down
one of its diagonals. Just sliced the diagonal plane and leaving
behind two pieces. What
are they called? Are they a wedge? The cube division looks like a 3D
isosceles right triangle
and the rectangular-solid divided looks like a 3d right-triangle-
solid.

Now I wonder if these figures have a formal name in math already,
rather than simply calling
them wedges?

Now the reason I want them is because two of them put together form
the cube or rectangular
solid and for which I can tile without any holes or gaps between. I
believe one of these is going
to be the maximum tiler in 3D.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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