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

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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.

Prismatic Versions of Part of a Tessellation Using Squares and 60-120-60-120 Rhombi

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Prismatic Versions of Part of a Tessellation Using Squares and 60-120-60-120 Rhombi

Above, the apparent size of the tessellation-prism does not change. In the next image, though, I set the controls of Stella 4d (the program I use to make these images, which you can try at http://www.software3d.com/Stella.php) to fit the image tightly, separately, in each still frame, causing a “breathing” effect. (Click on it if you wish to see it enlarged.)

Next, I added two red rhombi, one at the top and one at the bottom, stellated the result many times, and made one final .gif image, leaving the “breathing” effect on.

A Rhombicosidodecahedron, Augmented with Thirty Icosakaipentagonal Prisms

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A Rhombicosidodecahedron, Augmented with Thirty Icosagonal Prisms

When adding icosakaipentagonal prisms (those where the bases have 25 sides) to the thirty square faces of a rhombicosidodecahedron, the prisms can have one of two orientations. One is above, and here is the other one (click to enlarge):