Each pair is a different color. Because these decagons intersect in space, but do not meet at edges, they do not form a true polyhedron. They are merely a symmetrical configuration of twelve decagons in space, surrounding a central point.
I made this out a “true polyhedron” by hiding all the other faces from view. Before the hiding and recoloring of faces, this looked this way (you can click on it to enlarge it):
I used Stella 4d to make these images, and you can find that program at http://www.software3d.com/Stella.php.
Some polyhedral compounds are well-known, such as the compound of five cubes, while others are less famous. I had never heard of this compound before building one today (virtually, not as a physical model). However, a quick Google-search told me that I was not the first person to discover it.
Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
Those big round things aren’t circles. They are regular thirty-sided polygons, or triacontagons.