# Tag Archives: mathematical

# Octagonal Spirals

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

# A Rhombicuboctahedron Made of Lux Blox

This is my latest creation with my newest polyhedron-building tool, Lux Blox. The orange and blue “Lux squares” differ only in color, and here they represent the square faces of a rhombicuboctahedron. The triangular gaps represent that polyhedron’s triangular faces.

If you’d like to try Lux Blox yourself, the website to visit to buy them is www.luxblox.com. The last picture includes my hand to give a sense of scale to these models.

# An Octahedron Made of Lux Blox

This is the first model I built with Lux Blox, a modeling-system I’ve been checking out. If you’d like to try Lux for yourself, the website to visit to get them is https://www.luxblox.com/.

This is an octahedron with an edge length of two. The eight triangular faces are blue, while the edges of the octahedron are orange. Apart from their colors, all these pieces are identical — the basic Lux block, also known as a Lux square. With just this one block, you can build literally millions of things. I’m into polyhedra, so that’s what I’ll be building a lot of, but someone obsessed with dinosaurs could build models of those, as well. Lux Blox are *that* versatile.

The images above and below show the same Lux polyhedron, viewed from different angles.

# Sixteen {7/2} Star Heptagons

Two of the heptagrams are centered in the middle, while the other fourteen are smaller, and form a ring around the two in the center.

# Ten Pentagrams

The ten pentagrams meet at a common vertex in the center.

# Fourteen Heptagrams

The fourteen heptagrams, also known as {7/3} star heptagons, meet at a common vertex in the center of the whole diagram. I did the math using *Geometer’s Sketchpad*, and then colored the result using *MS-Paint*.

## Golden Triangles and Golden Gnomons

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## Circles, Triangles, and a Pentagon

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# Spectral Icosahedra

*Stella 4d: Polyhedron Navigator* has a “put models on vertices” function which I used to build this cluster of 61 icosahedra. If you’d like to try this software for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.