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

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An Arrangement of Heptagonal Prisms

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

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

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

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.

A Tessellation Featuring Regular Pentagons, Squares, Rhombi, and Concave, Equilateral Octagons

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Thanks and a tip of the hat to Livio Zucca, who gave me the idea for this tessellation.

Several Pencil Drawings

View From Behind Saturn
Multicellular
Smile
Math Art
Three Solids
Billow

Three Pencil Drawings

Tetratentacle
Spider
Serious Goose

Two More Pencil Drawings

Two O’Clock
Eukaryote

Two Drawings of People

A Woman in Profile
A Man

For three days this week and another three next week, during this round of standardized testing, my assigned task at work, for four to five hours each day, is to guard a locked door to the testing area. I’m not allowed to bring a computer, a cell phone, or even a book, so I brought a clipboard, with ample blank paper, and a handful of freshly-sharpened pencils. As a result, this mostly-mathematical blog will be detouring into drawings for a while. These were the first two.