This polyhedron has 24 faces: 12 pentagrams and 12 intersecting pentagons.
The surface of each pentagon is covered except for 5 rhombic areas.

If you want to make a paper model of this polyhedron, you need
12 pentagrams and 60 rhombi. The rhombi are easy to construct once you have
made a pentagram -- the edge lengths are equal to the exterior edge-length
of the pentagram and the larger internal angle is the same as the internal angle of
a pentagon, i.e. 108 degrees). If you have 6 colors of paper, you can assign one
color to each set of mutually parallel faces -- make 2 pentagrams and
10 rhombi of each color.

I also have an anaglyph version of this, to be viewed with
red-blue or red-green 3D glasses.

Mathematica was used to generate the input data for the POV-Ray ray-tracing program.