rhombicuboctahedron | RobertLovesPi.net

A Rhombcuboctahedron, with Its Square Faces Augmented By Hexacontakaitriacosioigonal Prisms, Together with Two Views of the Convex Hull of That Augmented Polyhedron

Image

A Rhombcuboctahedron, with Its Square Faces Augmented By Hexacontakaitriacosioigonal Prisms

The eighteen regular prisms (whose bases each have 360 sides) augmenting the square faces of the rhombcuboctahedron hidden in the center, above, can be oriented in more than one way. I simply chose the orientation I liked best.

After that, I took the convex hull of the figure above, just to see what would happen. With each different face type having a different color, it looks like this (click to enlarge either or both images below, if you wish):

I then chose a different color-scheme. Instead of giving faces of each type a different color, I colored the faces by their number of sides. This led to a more pleasing result:

The things that look like rounded yellow rectangles are an illusion; polyhedra don’t have curved faces. They are actually numerous thin, adjacent, near-coplanar rectangles with the same color.

All three images were created with Stella 4d, software available at http://www.software3d.com/Stella.php.

Slow Dissection of a Loosely-Defined “Faceted” Rhombcuboctahedron

Image

If you look at the second image from the post two entries ago, and wonder what it would look like without the pink faces, wonder no longer: it’s what you see above.

Next, the red polygons are hidden, and this is what is left (you may click these smaller images if you wish to enlarge them).

The green faces are hidden next.

The next step is to remove the pink faces visible in the interior.

Next, removal of the blue faces leaves only the yellow ones left.

The last step: change the color scheme, so as to more easily be able to tell one face from another.

All of this polyhedron-manipulation, I did with Stella 4d, software I consider an indispensable research-tool. It is available at http://www.software3d.com/Stella.php.