Three Views of The 27th Stellation of the Small Icosihemidodecahedron

First, here is this polyhedron colored by face type.

Next, the faces are each given their own color, except for parallel faces, which have the sme color.

Finally, here’s what this polyhedron looks like in “rainbow color mode.”

I made these virtual models using Stella 4d, which you can try for yourself right here.

A Non-Convex Polyhedron With Sixty Each of Two Types of Kites

I made this by stellating the small icosihemidodecahedron, one of the uniform solids, once. I did this using Stella 4d, which you can try for free right here.

A Great Rhombicosidodecahedron, Augmented With Pyramids

I made this using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

A Polyhedron Formed by Repeatedly Stellating the Triakis Octahedron, Along With Its Dual

I made these virtual models using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.

A Cube, Held Prisoner by a Stella Octangula

I made this three-part compound using Stella 4d (available here) to repeatedly tetstell a truncated octahedron.

A Symmetrohedron Featuring Three Regular Pentagons, One Regular Hexagon, One Equilateral Triangle, and Three Each of Two Different Isosceles Trapezoids

I’m 90% sure this hasn’t been found before. It has three-fold pyramidal symmetry.

Here is its net.

I used Stella 4d to make this. You can try this program for free at this website.

A Three-Part Compound Derived From the Rhombic Triacontahedron

I made this using Stella 4d, which you can try for free right here. It’s a continuation of the post immediately before this one.

Five Polyhedra Derived From the Rhombic Triacontahedron

Starting with the rhombic triacontahedron, I tetstelled it three times, and found this unusual polyhedron. It has eighteen faces: six parallelograms, and twelve trapezoids.

Here’s what happened when I used Stella 4d‘s “try to make faces regular” function on the polyhedron above.

This solid has six rhombic faces, and twelve faces which are kites. Here is its dual:

Next, I returned to the red-and-yellow solid above, and tetstelled it numerous times, producing a compound of a cube and a distorted rhombic dodecahedron.

A few more tetstells produced this interesting three-part compound.

If you’d like to try Stella yourself, the website to visit is http://www.software3d.com/Stella.php. There’s a free trial download there.

This Blog Now Has a Tip Jar

WordPress charges me $480 every two years to host this blog (because it’s so big), and keep it ad-free. I’m now accepting donations to offset this cost. To access the donation site, just look on the right side of the menu bar at the top of any page here, where it says “Tip Jar,” click on those words, and then look for the blue link.

This is completely voluntary. There’s no “premium” content to unlock. Those who choose not to donate can still access everything here. Those who do donate receive my gratitude, along with the warm, fuzzy feeling one gets from doing a good deed.

Donations are not tax-deductible.

A Two-Part Compound, Derived From the Rhombicosidodecahedron

This is the familiar compound of the icosahedron and dodecahedron, except with both of those solids augmented on each face with short pyramids. I made it using Stella 4d, which you can try at this website.