Spectral Tessellation of Rhombi

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Tessellation 4, 5, 6

Posted on 17 October 2020 by RobertLovesPi

The tessellation above is shown in primary colors. The one below is rendered in shades of blue.

A Tessellation of Regular Hexagons, Squares, and Triangles

Posted on 10 October 2020 by RobertLovesPi

I wonder if other people find tessellation relaxing?

A Tessellation of Regular Polygons

Posted on 10 October 2020 by RobertLovesPi

This tessellation is made only of regular polygons: triangles, squares, and dodecagons.

A Rhombic Dodecahedron Decorated with Golden Mandalas

Posted on 27 September 2020 by RobertLovesPi

To make this, I used Stella 4d: Polyhedron Navigator to take the image I blogged here, and then project it onto the faces of a rhombic dodecahedron. Next, I put that polyhedron into motion for the .gif shown below.

If you’d like to give Stella a free try, the site to visit is http://www.software3d.com/Stella.php.

Octagonal Spirals

Posted on 13 September 2020 by RobertLovesPi

This is a modification of the well-known tessellation of the plane with squares and regular octagons.

A Tessellation of Regular Decagons and Bowtie Hexagons

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A Tessellation of Concave, Equilateral Pentagons, Together with Tetraconcave, Equilateral Octagons

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A Concave Polyhedron Featuring Eight Regular Dodecagons

Posted on 17 August 2020 by RobertLovesPi

110 faces 8 dodec 6 rectangles 96 triangles

This 110-faced polyhedron has, in addition to the eight regular dodecagons, six rectangles, and 96 triangles. I made it using Stella 4d, a program you can try for free, as a demo version, at http://www.software3d.com/Stella.php. I wish I could remember how I made it!

Fortunately, I have many friends who are more knowledgeable than I, when it comes to mathematics. Perhaps one of them will be able to solve this mystery.

A Symmetrohedron Featuring Regular Heptagons, Regular Hexagons, Irregular Hexagons, and Irregular Pentagon-Pairs

Posted on 2 August 2020 by RobertLovesPi

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

This particular symmetrohedron features twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.