The faces of this are twelve interpenetrating regular pentagons, and twenty 6/2-gons (a type of star hexagon that looks like a radiation symbol).
This was created using software, Stella 4d, which you can find and try at http://www.software3d.com/stella.php.
The kites to use have side lengths in a ratio of one to the square root of three, and angle measures of 60, 90, 120, and 90 degrees.
Created using software here: http://www.software3d.com/stella.php.
(Software credit: see http://www.software3d.com/stella.php)
http://www.software3d.com/stella,php — that’s the place to go to try the software used to make this
RobertLovesPi.net 