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

# Tag Archives: heptagon

# 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.

# Sunflower Fourteen

This mathematical illustration of a sunflower is made of fourteen regular heptagons, fourteen irregular pentagons, and a single tetradecagon.

## A Christmas Wreath Made of Heptagons and Heptagrams

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# Four Polyhedra Featuring Heptagons

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

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.

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.

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.

# A Tetrahedrally-Symmetric Polyhedron Featuring Heptagons

Created using *Stella 4d: Polyhedron Navigator*; see this website to try it for yourself!

# 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.