I’d like to find a polyhedron with the same number of faces as there are days of the year. This is the closest I’ve come, so far.
The software I used, Stella 4d, may be purchased at http://www.software3d.com/Stella.php. There is also a free trial download available.
I wonder if your chances will be better on leap year. 🙂
Actually, they will! Odd numbers of faces don’t often (never?) appear in symmetrical polyhedra of the tetrahedral, cuboctahedral, or icosidodecahedral type. Those are the type I favor. Asymmetrical polyhedra can be really ugly, even if only regular polygons are used. Check the Wikipedia article on “Johnson solids” to see what I mean.