Twelve of the faces of this polyhedron are star pentagons, and they are easy to spot. The other sixty faces are isosceles trapezoids, and they’re harder to find because parts of them are hidden inside in the solid. The image below shows where these trapezoids can be found.
I made this using Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.
I first named the rhombic octagonoid, a ninety-faced zonohedron, right here. I’ve added a new twist to it now, though, and that is to expand this polyhedron using twenty equilateral triangles. This causes the octagons of the rhombic octagonoid to become decagons. This new solid has 110 faces, and is not a zonohedron, although it is a “zonish” polyhedron. The only faces it has which are not zonogons are the triangles.
I built this new polyhedron with Zome. If you’d like to try out Zome for yourself, the website to visit is at http://www.zometool.com.
RobertLovesPi.net 