Four Polyhedra, Each With Seven-Fold Dihedral Symmetry

First, the heptagonal antiprism.

The rest of the polyhedra in this post were made from this antiprism, using the functions available in Stella 4d: Polyhedron Navigator, such as stellation and faceting. If you’d like to try this program yourself, you can do so, free, at http://www.software3d.com/Stella.php.

A Non-Convex Polyhedral Cluster Featuring Regular Heptagons, With a Puzzle

I stumbled upon this while playing with Stella 4d: Polyhedron Navigator, a program you can try for free at https://www.software3d.com/Stella.php. It’s difficult to herd regular heptagons.

There’s an obvious question raised by this image: what are the components of the polyhedral cluster, especially the one with heptagonal faces? Comments on this would be appreciated, especially ones with images of the components.

42 Heptagons

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A Polyhedron With 154 Faces, Twenty of Which Are Regular Heptagons

I made this using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.

A Ring of Fourteen Heptagonal Prisms

I made this using Stella 4d, which is available here.

An Agglomeration of Triangles and Six Oblique Heptagonal Prisms

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I made this using Stella 4d, which you can try for free right here.

A Polyhedron Featuring a Dozen Regular Heptagons and a Whole Mess of Quadrilaterals

There are four different shapes of quadrilaterals here, but they have one thing in common: there are twelve of each of them. Add those 48 quads to the twelve regular heptagons, and that gives a total of 60 faces. I found this polyhedron while playing with the snub dodecahedron, using Stella 4d: Polyhedron Navigator, a program you can try for free right here.

In the image below, each of the four types of quadrilateral appears with its own color.

Tessellation Featuring Squares, Regular Heptagons, and Two Types of Four-Pointed Stars

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Tessellation Featuring Regular Heptagons and Triangles, as Well as Four- and Six-Pointed Stars

It’s difficult to work regular heptagons into a symmetrical pattern, so I’m quite proud of this one.

A 56-Faced Polyhedron Featuring Eight Regular Heptagons

I made this using Stella 4d, which you can try for free right here.