About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

Three Views of a Modified Great Rhombicosidodecahedron

To make these using Stella 4d (available here), I started with the great rhombicosidodecahedron, then used the “morph duals by expansion” function on it — twice. Here’s the result, shown with coloring done by face type.

The next one has faces colored by number of sides.

Finally, here’s one shown in rainbow color mode.

A Symmetrohedron With 152 Faces

The 152 faces of this symmetrohedron include twelve regular decagons, twenty regular hexagons, and 120 irregular quadrilaterals arranged in thirty groups of four quads each. I made it using Stella 4d, which you can download here as a free trial version.

Two Polyhedral Compounds Derived From Catalan Solids

The second stellation of the dysdyakis triacontahedron, seen above, is an interesting two-part polyhedral compound. The dysdyakis triacontahedron is one of the Catalan solids, and is the dual of the great rhombicosidodecahedron.

There’s also a “little brother” to this first compound — it’s the second stellation of the dysdyakis dodecahedron, which is the dual of the great rhombicuboctahedron. Like its “big brother,” it’s a two-part compound. It is shown below.

Interestingly, the components of these two compounds are “stretched” versions of two other Catalan solids: the pentagonal hexecontahedron (dual of the snub dodecahedron), and the pentagonal icositetrahedron (dual of the snub cube).

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

Two Half-Visible Catalan Solids

The Catalan Solids shown here are the dysdyakis dodecahedron (dual of the great rhombicuboctahedron) and the dysdyakis triacontahedron (dual of the great rhombicosidodecahedron). In each one, all the faces are scalene triangles, and half of them have been rendered invisible, so that you can see the inside view of faces on the far side of each polyhedron. The remaining faces are shown in “rainbow color mode.”

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

Two Different Double Cuboctahedra, and Their Duals

There are at least two ways to make a double cuboctahedron. One way is to join two cuboctahedra at a square face.

The dual of a single cuboctahedron is a rhombic dodecahedron. The dual of this first double cuboctahedron, however, doesn’t look like a rhombic dodecahedron at all.

Another way to make a double cuboctahedron is to join two cuboctahedra at a triangular face.

Here’s the dual of the second type of double cuboctahedron.

I created these four polyhedra using Stella 4d, a program you can download and try for free, as a trial version, at this website.

The Latest Episode (With Bandit the Kitten and The Flaming Lips)

So we’re watching the latest episode of Star Trek: Picard tonight, as we do every Thursday night, when Bandit the Kitten decides to tear a gash in my leg with his incredibly sharp claws.

I waited until the show was over before pouring rubbing alcohol on it, which, of course, stung quite sharply,

In that moment of stinging, I realized that there’s a song for this occasion. It’s by The Flaming Lips.

My favorite lines in this song, “The Gash,” form a question: “Will the fight for our sanity / Be the fight of our lives?” With this kitten here in our apartment, it just might be exactly that.