Pseudoglobes on rhombic dodecahedra, gnomonic projection.

A rhombic dodecahedron is not a regular polyhedron, since its
twelve identical faces are diamonds. It and
the cuboctahedron comprise
a pair of dual polyhedra: for each face of one there is a
corresponding vertex in the other, and vice versa. This solid appears in
nature in honeycombs, where every cell consists of half a rhombic
dodecahedron topped by a hexagonal prism. A honeycomb has two
layers of parallel cells opening in opposite directions, and the
bottom of each cell nests between the bottoms of three cells of
the opposite layer. Coupled with the choice of hexagonal prisms,
this is relevant for efficient use of beeswax, as the rhombic
dodecahedron, like the
cube and
the truncated octahedron,
can tesselate three-dimensional space: multiple copies can be
juxtaposed to fill any volume.

The rhombic dodecahedron has large faces and can be easily built.
However, please read the
generic assembly tips before beginning.
You might also learn something about
polyhedral
maps and other map projections.