Tetradecahedron

mesh: Topmod v2, Blender 2.74
modelling: Blender 2.74
rendering: Luxrender 1.4
post production: none
design time: 2 evenings
render time: 31 hours, 5000 spp (Intel Q6600)
resolution: 1920x1080

Tetradecahedron (14 sides) with some internal structure.  If the hexagons were regular (equal on all sides), this would be a truncated octahedron.  The background was actually a mistake but I kept it since it looked somewhat unique.