RobertLovesPi.net

Polyhedra, tessellations, and more.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

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

Posted on 28 May 2021 by RobertLovesPi

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

Posted on 23 May 2021 by RobertLovesPi

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

Posted on 15 May 2021 by RobertLovesPi

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

A Starry Icosidodecahedron

Posted on 15 May 2021 by RobertLovesPi

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.