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Five Versions of a Tessellation Using Squares and Equilateral Triangles

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Tessellation Using Squares and Triangles

I used four other color-schemes with this same tessellation, and those other images are shown below.

Squares and Triangles

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Squares and Triangles

Here’s what it looks like with different colors (click to enlarge it):

Tessellation of the Plane with Regular Hexagons, Squares, and Tetraconcave, Equilateral Octagons, #1

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Tessellation of the Plane with Regular Hexagons, Squares, and Tetraconcave, Equilateral Octagons

If you’d like to see the second version of this tessellation, made over a decade later, simply click right here.

Tessellation Using {8/3} Star Octagons and Squares

The tessellation of the plane which uses regular convex octagons and squares is well-known. This related tessellation, however, is not. I didn’t know it existed until I stumbled across it . . . although I very much doubt I am the first person to do so.

Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons II

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← Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons II

Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

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Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

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Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

Prismatic Versions of Part of a Tessellation Using Squares and 60-120-60-120 Rhombi

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Prismatic Versions of Part of a Tessellation Using Squares and 60-120-60-120 Rhombi

Above, the apparent size of the tessellation-prism does not change. In the next image, though, I set the controls of Stella 4d (the program I use to make these images, which you can try at http://www.software3d.com/Stella.php) to fit the image tightly, separately, in each still frame, causing a “breathing” effect. (Click on it if you wish to see it enlarged.)

Next, I added two red rhombi, one at the top and one at the bottom, stellated the result many times, and made one final .gif image, leaving the “breathing” effect on.

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.)