The polyhedron shown above is the final stellation of the icosahedron, while the one below is the rhombic triacontahedron’s final stellation. I made these using *Stella 4d*, which you can try for free at http://www.software3d.com/Stella.php.

# Tag Archives: geometry

# A Symmetrohedron Featuring Twenty Equilateral Triangles, Twelve Regular Decagons, and Sixty Isosceles Triangles

I made this using *Stella 4d*, which you can try for free right here: http://www.software3d.com/Stella.php.

# An Augmented and Excavated Icosidodecahedron

To make this, I augmented the pentagonal faces of an icosidodecahedron with pyramids, while the triangular faces of this icosidodecahedron had pyramids excavated from them. The result, as you can see, looks like an icosahedron with tetrahedral indentations is the middle of each face. I made it using *Stella 4d*, which you can try for free at http://www.robertlovespi.net/Stella.php.

# A Rhombicosidodecahedron, With Its Faces Augmented by Inverted Cupolae

Here’s a second view, in “rainbow color mode.”

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

# A “Near Near-Miss” With 152 Faces

This isn’t quite a near-miss to the Johnson solids, so I’m calling it a “near near-miss.” It could also be classified as a symmetrohedron. The pentagons and triangles are regular, but the red triangles have edges which are about 12% longer than those of the yellow triangles. The blue faces are isoceles trapezoids.

I found it while playing around with the great rhombicosidedcahedron using *Stella 4d*, which you can try for free right here.

# An Icosidodecahedron, Augmented with Pentagonal and Triangualar Cupolae

I made this using *Stella 4d*, which you can try for free at this website.

Here’s another version of the same polyhedron, made using “rainbow color mode.”

# A Second and Third Excavated Great Rhombicosidodecahedron

In the previous post (here), I showed a great icosidodecahedron with its hexagonal faces replaced by inward-facing triangular cupolas. This one is similar, but the excavations take place on the decagonal faces, and take the shape of pentagonal cupolas.

Lastly, here’s a great rhombicosidecahedron with cupola-excavations performed on both its hexagonal and decagonal faces.

I made these images using *Stella 4d*, which you can try for free here.

# An Excavated Great Rhombicosidodecahedron

This great rhombicosidodecahedron has had its hexagonal faces replaced by indentations, each the shape of a triangular cupola. I made it using *Stella 4d*, which you can try for yourself, free, at this website.

# Two Chiral Symmetrohedra Derived From the Snub Dodecahedron

Each of these symmetrohedra has 302 faces. The one above was created by using the “morph duals by expansion” function, on the snub dodecahedron, in* Stella 4d*, the program I use to manipulate polyhedra (go here if you want to download a free trial of this software). It has twelve regular pentagons, sixty almost-square rectangles, and eighty equilateral triangles, along with ninety more obviously non-square rectangles, and sixty irregular pentagons.

I next used Stella’s “try to make faces regular” function, which produced this result:

This second polyhedron has 72 regular pentagons as faces, along with 20 equilateral triangles, 60 narrow isosceles triangles, and 150 irregular quadrilaterals. That’s 92 regular faces, in each of these two polyhedra.

# A Polyhedron Featuring Twenty-Four Regular Pentagons and Sixty Convex Hexagons

I made this using *Stella 4d*, which you can for yourself, as a free trial download, right here: http://www.software3d.com/Stella.php.