A Fractal Tessellation of Golden Triangles, Golden Gnomons, and Regular Decagons

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A Radial Tessellation of the Plane Using Squares and 45/135 Degree Rhombi

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This is an adjustment and extension of the radial tessellation shown in the most recent post here. I am now confident that this pattern could be extended outward, without limit.

A Radial Octagonal Tessellation of Squares and Rhombi

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I believe this can be continued, outward, indefinitely. I also believe it is aperiodic. However, I do not have a proof for either of these conjectures.

Three Times Eight Is Twenty-Four

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A Tessellation Featuring Regular Octagons, Regular Dodecagons, and “Bowtie” Hexagons

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A Fractal Tessellation Featuring Regular Pentagons and Golden Gnomons

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The yellow triangles are golden gnomons, while the blue triangles have angles of 108, ~26.3, and ~45.7 degrees.

A Tessellation Featuring Regular Octagons, Regular Hexagons, Squares, and Isosceles Trapezoids

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A Tessellation Featuring Regular Octagons, Regular Hexagons, and Convex Pentagons

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Eights

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This began with an {8/3} star octagon. It then started spreading.

A Starry Icosidodecahedron

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The stars on the pentagonal faces were drawn using Geometer’s Sketchpad and MS-Paint. The icosidodecahedron itself was created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.