This polyhedron can be made from 5 different colors. Each pair of truncated faces (8 hexagons) will be a different color (four of the colors). The truncations (8 square faces) will be a fifth color.
To see the full sized template click on this image:
You will need to cut 8 of hexagonal faces. Make two hexagonal faces of each of the four colors. You will need 6 square faces that are all the same color.
You can assemble this polyhedron by attaching 4 hexagonal faces to one of the square faces. The 6 edges of each hexagonal face will be glued alternately to a square and then another hexagonal face. All of the square faces will be surrounded by hexagons.
Position each pair of same-colored hexagonal faces on opposite sides of the polyhedron. The placement of same-colored hexahedral faces should be apparent. Parallel planes will now contain hexagonal faces of the same color.