Tags » Icosahedron

An Unsolved Problem Involving the Icosahedron and the Dodecahedron, and Their Circumscribed Spheres

This is apparently a problem, posed by Gregory Galperin, which went unsolved at the Bay Area Math Olympiad in 2005. I haven’t solved it yet, but I’m going to try, as I work on this blog-post. 686 more words


The Cube / Icosahedron Compound

I made this rotating .gif file using Stella 4d. You can try this software for itself at http://www.software3d.com/Stella.php.


30 Unit Icosahedron

Edge Module Icosahedron designed by Tomoko Fuse
Folded by Franck Ramaharo

Unit Origami

An Icosahedron, Augmented with Twenty Triangular Cupolae, Together with Its Dual

After making the above polyhedron using Stella 4d (a program you can try for free at www.software3d.com/Stella.php), I checked its dual, which is shown below. 22 more words


Sacred Geometry

The strands of our DNA, the cornea of our eye, snow flakes, pine cones, flower petals, diamond crystals, the branching of trees, a nautilus shell, the star we spin around, the galaxy we spiral within, the air we breathe, and all life forms as we know them emerge out of timeless geometric codes. 221 more words

Sacred Geometry

A Compound of an Icosahedron and the First Stellation of the Rhombic Triacontahedron

I stumbled across this compound yesterday, an example of exploratory polyhedral manipulation using Stella 4d producing an unexpected result. If you would like to experiment with a free trial download of this program, before deciding whether or not to purchase the fully-functioning version, simply click here:   6 more words