An Octahedral Lattice of Rhombic Triacontahedra, Vanishing By Fifths

An Octahedral Lattice of Rhombic Triacontahedra, Vanishing By Fifths

These rhombic triacontahedra (RTCs) are each colored with the symmetrical five-color scheme for that polyhedron. It causes each color to appear six times on each RTC, in positions such that, for a single RTC, a centered x, y, and z axis can penetrate the centers of all six same-color faces.

Since there are five colors, this virtual model may be removed in fifths. The first to go are the green rhombi. (Each of these may be enlarged with a click.)

Augmented Rhombic Triaconta

The next to be removed are the yellow rhombi.

Augmented Rhombic Triaconta

The red ones are next to go.

Augmented Rhombic Triaconta

One more fifth vanishes, and only the blue faces are left.

Augmented Rhombic Triaconta

Finally, they are removed as well, but with edges and vertices now shown for the first time, for, otherwise, you’d see nothing here.

Augmented Rhombic Triaconta

Software credit:  all images here were created using Stella 4d: Polyhedron Navigator, my favorite polyhedron-manipulation tool. You may try it for yourself as a free trial version, or purchase the fully-functioning version, at http://www.software3d.com/Stella.php.

 

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s