A Polyhedron Featuring Sixty Heptagons, a Dozen Decagons, Thirty Octagons, and 120 Rectangles, Split Between Two Types at Sixty Each

I made this using Stella 4d: Polyhedron Navigator. This program is available as a free trial download at http://www.software3d.com/Stella.php.

The Dual of a Geodesic Rhombicosidodecahedron

This polyhedron has, as faces, a dozen regular pentagons, thirty rhombi, and sixty irregular heptagons. I made this using Stella 4d, which is available as a free trial download at http://www.software3d.com/Stella.php.

Four Polyhedra Featuring Heptagons

Heptagons only appear infrequently in interesting polyhedra. I recently found a few that I like.

Icosidodeca 2nd tetstell with heptagons and triangles is pyritohedral.gif

To form the first of these solids, shown above, I started with the icosidodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and then stellated it twice using Stella 4d (available here). To obtain the model shown below, which also features heptagons and triangles, I stellated it once more. Both of these polyhedra have pyritohedral symmetry.

Icosidodeca 3rd tetstell with heptagons and triangles is pyritohedral.gif

To form the next model shown, I began with an rhombicosidodecahedron, set it to tetrahedral symmetry, and stellated it eight times. This produces a chiral solid with tetrahedral symmetry.

Stellated Rhombicosidodeca 8th tetstell features 8 heptagons tet symmetry.gif

For the last of these four polyhedra featuring heptagons, I began with the snub dodecahedron, dropped the symmetry of the model down from icosahedral to tetrahedral, and then stellated it sixty-one times. The resulting solid is chiral, with tetrahedral symmetry.

Snub Dodeca 61st tetstell.gif

Three Polyhedra Featuring Heptagons

For some reason I do not fully understand, polyhedra featuring heptagons, even if irregular, do not appear often, at least not in my geometrical investigations — so I was pleased to find these three, using Stella 4d: Polyhedron Navigator, available at http://www.software3d.com/Stella.php.