Open Octahedral Lattice of Cubes and Rhombicosidodecahedra

This pattern could be continued, indefinitely, into space.

Augmented Rhombicosidodeca

Here is a second view, in rainbow color mode, and with all the squares hidden.

Augmented Rhombicosidodeca rcm

[These images were created with Stella 4d, software you may buy — or try for free — right here.]

“Math Problems for Fun”: The Source of My Blog’s New Header-Image

cyanide and happiness without black border

I don’t usually post the work of others here, but, since I am now using this as my blog’s header-image (in slightly altered form), it seemed appropriate to make an exception for this cartoon, in its original format. I didn’t know that the cartoonists at Cyanide and Happiness monitored my life, but, clearly, that guy in the blue shirt is me!

Arch (a painting from 2003)

Arch 2003

Media used: acrylic on canvas.

Although I have not yet seen it in person, this painting is based on images I have seen of Delicate Arch, in Utah’s Arches National Park.

Discovery (a painting from 2002-2003)

 

discovery 2002-2003

Media used: acrylic on canvas.

Older Birthday Stars, From When I Was Younger

I started this blog in July of 2012, so the birthday stars I made in January 2012 (when I turned 44) and January 2011 (when I turned 43) did not appear here in those years. I found them, though, and will post them now.

The first two are different colorings of a 44-pointed star, from January 12, 2012, the day I turned 44:

birthday star 44 from 2012 Bbirthday star 44 from 2012

These three are different color-versions of 43-pointed stars, from a year earlier — January 12, 2011:

43 star{36_slash_17} schlafli symbol star 2012

43

I turn 48 today, so please visit the post right before this one, if you’d like to see this year’s birthday stars. =)

My Birthday Stars for 2016

This year, I’m continuing my personal tradition of making stars on my birthday with numbers of points which increase each year. I’ve done this for years, and it’s based on a game I started when I turned three, and claimed the three stars of Orion’s belt as my personal property, on the grounds that they were obviously put in the sky for my benefit. Most recently, a year ago, when I turned 47, I posted a 47-pointed star on this blog.

I’m turning 48 today, so here are a couple of different colorings of 48-pointed stars containing segments through the center, {6/2} compound-triangle stars, and {8/3) star octagons, made possible by the fact that 48 = (6)(8).

star 48b

star 48a

Of course, I am turning 48 on my 49th birthday (and if that makes no sense to you, here’s the explanation), so this year I also made 49-pointed stars. They are based on 49 being the square of seven, and so contain seven each of the two types of star heptagram possible, in two different colors. For this star, also, I made two versions.

star49a

star49b

Isosceles Interference Pattern (two versions)

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isosceles interference pattern

isosceles interference pattern

Interference Spider with Two Eyes Showing (from 2013)

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spider interference pattern 2013

Every now and then, I find something I created some years ago, but never blogged here. This is another such piece, which I made in 2013 (using Geometer’s Sketchpad and MS-Paint), but did not name until today.

A Spectrum of Pentagons, Backed By Black & White

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pentagons

Two Color-Patterns of a Tessellation Using Squares, Rhombi, Equilateral Hexagons, Tetraconcave Octagons, and Regular Octagons

new tessnew tess 2