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

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):

Convex hull

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:

Convex hugll

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.

 

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