Author Archives: RobertLovesPi

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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 Tessellation Featuring Regular Pentagons, Regular Hexagons of Two Sizes, Isosceles Trapezoids, and Equilateral Octagons

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A Tessellation of Regular Hexagons, Regular Heptagons, Convex Pentagons, and Large Areas of Negative Space

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If you don’t want to view part of this as “negative space,” you can instead view the black regions as concave heptaicosagons (27-gons).

A Tessellation of the Plane Using Regular Hexagons and Regular Pentagons, Along With Concave, Equilateral Octagons

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A Polyhedron With 182 Faces and Icosidodecahedral Symmetry

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This polyhedron contains, as faces, 12 regular decagons, 20 regular hexagons, 30 squares, and 120 irregular hexagons. I made it using Stella 4d, which you can try for free at this website.

A Tetrahedral Symmetrohedron

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This symmetrohedron has four faces which are regular hexagons, 24 which are regular pentagons, and four which are equilateral triangles. It also has twelve faces which are acute isosceles triangles, as well as twelve more which are obtuse isosceles triangles. I made it using Stella 4d, which you can try for free here.

A Tessellation Featuring Regular Hexagons, Squares, Equilateral Triangles, and Rhombi

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An Arrangement of Heptagonal Prisms

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Here is its dual.

I made these using Stella 4d: Polyhedron Navigator, a program you may try for free at http://www.software3d.com/Stella.php.

Six of Seven

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This 31-faced polyhedron is unusual in that it features six regular heptagons as faces. I made it using Stella 4d, which you can try for free at this website.

Five of Seven

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This polyhedron is unusual in that it has five regular heptagons as faces. It has twenty-two faces in all. It was created using Stella 4d, software you can try for free right here.

Compound of Four Elongated Tetrahedra

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To make this, I started with a dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, then stellated it five times. Finally, I chose “color as a compound” for the color-settings. I did this using Stella 4d, software you can try for free right here: http://www.software3d.com/Stella.php.