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.

Meditations Upon a Ring of Hendecagons

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Tessellation Featuring Regular Pentadecagons

Posted on 15 September 2019 by RobertLovesPi

The blue polygons are regular pentadecagons, and the yellow polygons are irregular dodecagons. There are also equilateral hexagons (orange), red squares, and black concave pentagons.

Tessellation of Regular Dodecagons and Tetraconcave, Equilateral Octagons

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Two Rhombic Polyhedra with Tessellated Faces

Posted on 8 September 2019 by RobertLovesPi

These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).

I made both of these using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.

Yellow Star Tessellation

Posted on 8 September 2019 by RobertLovesPi

In this tessellation, the hexagons, pentagons, and squares are all regular. The irregular polygons are equilateral decagons, as well as equilateral and concave tetrakaiicosagons.

Five Variants of the Compound of Two Tetrahedra

Posted on 25 August 2019 by RobertLovesPi

This is the compound of two tetrahedra, also known as Johannes Kepler’s Stella Octangula.

I found the five variations of this polyhedral compound shown below, located deep within the stellation-series of the great rhombicuboctahedron.

These .gif images were all made using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

Tessellation of {8, 3} Star Octagons, and Two Sizes of Squares

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Four, Six, Nine, and Eighteen

Posted on 21 July 2019 by RobertLovesPi

This mathematical illustration includes two shapes of rhombi (orange and green), isosceles trapezoids (blue), regular hexagons (yellow), regular enneagons (red), and a single regular octadecagon (violet).