There are exactly five combinatorial types of polyhedra that can fill three d imensional space. (Two polyhedra are of the same combinatorial type if they have the same numbers and kinds of faces, fitted together according to the same reci pe.)
<P> [LINK TO, or insert, Figure 19, p. 158, "On the Shoulders of Giant s.] <P>
The best way to understand how these polyhedra fill space is to make models a nd try to do it!
Here is a fold-out model for the polyhdron on the right, a <I> truncate d octahedron</I>.
<P> Insert diagram.<P>