Recently, someone who follows my blog asked for my permission to use one of the images here (a tessellation featuring regular heptagons, etc.) as the artwork to accompany a piece of music he created. I granted permission without hesitation, and am now posting a link to his song, Heptagon Heaven’s “Destroy the System.”
Tag Archives: heptagon
Two Polyhedra Which Feature Heptagons
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It’s unusual to encounter heptagons in any survey of polyhedra . . . so I made a couple. I didn’t see any reason to limit myself to regular heptagons, though.
I made these using Stella 4d, which is available at http://www.software3d.com/Stella.php.
A Tessellation Using Tetraconcave Octagons, Convex Hexagons, and Concave Heptagons
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98-Faced Polyhedron Featuring Heptagons
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There are, as faces, 24 irregular heptagons, 6 irregular octagons of one type, and 12 of another, 24 rectangles of one type, and 24 of another, and 8 equilateral triangles. This was made using Stella 4d, which you may try or buy at http://www.software3d.com/Stella.php.
42-Faced Polyhedron Featuring Heptagons
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The blue faces are irregular heptagons, and are twenty-four in number. There are twelve of the green rhombi, and six of the red squares. This was made using Stella 4d, which you may try or buy at http://www.software3d.com/Stella.php.
A Tessellation Featuring Regular Heptagons
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Regular heptagons, of course, can’t tile a plane by themselves. Of all tessellations of the plane which include regular heptagons, I think this is the one which minimizes between-heptagon gap-size (the parts of the plane outside any heptagon). However, I do not have a proof of this. The shape of each of the polygons which fill the “heptagon-only gaps” is a biconcave, equilateral octagon. With these octagons, this is a tessellation, but without them, it wouldn’t fit the definition of that term.
[Later edit: on Facebook, a friend showed me two others with smaller gap-sizes. In other words, the conjecture above has now been shown to be wrong.]
Mandala Based On Heptagons
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Can you find the irregularities in the coloring-pattern? If so, please describe them in a comment.
Twenty Hexagons with Heptagrammic Designs
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The design on the hexagons appeared in the last post here, and was created using Geometer’s Sketchpad and MS-Paint. After that, I used another program, Stella 4d, to place these images on the hexagons of a truncated icosahedron, render the pentagons invisible, and create this rotating .gif file.
Stella 4d may be tried and/or purchased at http://www.software3d.com/stella.php.
Ringed Heptastar
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Heptagon-based Op Art
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