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Octagon Tessellation

This tessellation is made entirely of octagons. Half of them are regular, while the other half are equilateral and tetraconcave.

A Tessellation Using Tetraconcave Octagons, Convex Hexagons, and Concave Heptagons

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A Chiral Tessellation of Tetraconcave Octagons, Convex Hexagons, and Concave Heptagons

Symmetrohedron Featuring Eighteen Regular Octagons, Eight Equiangular Hexagons, and Twenty-four Isosceles Trapezoids

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Symmetrohedron Featuring Eighteen Regular Octagons, Eight Equiangular Hexagons, and Twenty-four Isosceles Trapezoids

The regular octagons are of the same size, but of two different types, when one considers the pattern of other faces surrounding them. This is why six of them are yellow, and twelve are red.

If the hexagons and isosceles trapezoids were closer to regularity, this would qualify as a near-miss to the Johnson solids, but it falls short on this test. Is is, instead, a “near-near-miss” — and not the first such polyhedron to appear on this blog, either.

(Image created with Stella 4d — software you can try yourself at http://www.software3d.com/Stella.php.)

A Symmetrical Arrangement of Regular Octagons, Triangles, and Squares

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A Symmetrical Arrangement of Regular Octagons, Triangles, and Squares

This contains twelve octagons, six squares, and eight triangles. The “holes” in it keep it from being a true polyhedron, but it is my hope than further study of this arrangement may lead to the discovery of new, interesting, and symmetrical polyhedra.

(Image created with Stella 4d — software you can try yourself at http://www.software3d.com/Stella.php.)