A Near-Miss to the Johnson Solids, Which I’m Naming the Ditrated Dodecahedron, Part One | RobertLovesPi.net
I had a strange mishap recently with a member of my large collection of polyhedral dice. This hollow d12 fell apart, into two panels of six pentagons each. I held them together at vertices, rotating one of the panels slightly. Those gaps aren't rhombi, because their four vertices are noncoplana..
A Symmetrohedron With 62 Faces | RobertLovesPi.net
In this solid, the quadrilaterals are all squares, and the red triangles are regular. The only irregular polygons are the dark blue triangles, which are obtuse and isosceles. I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
Craters on the Near Side of the Moon, on the Faces of a Rhombic Enneacontahedron | RobertLovesPi.net
Moon image from https://www.usgs.gov/news/national-news-release/usgs-releases-first-ever-comprehensive-geologic-map-moon. Polyhedron created using Stella 4d: Polyhedron Navigator, which you can try for free at this website.
The Five Platonic Solids, Each Surrounded by Rhombicosidodecahedra | RobertLovesPi.net
First, the tetrahedron. Next, the cube, with each square face augmented by a single rhombicosidodecahedron. Next, this same operation is performed on an octahedron. Next, the dodecahedron. Finally, the last of the set, centered on an icosahedron. This one is my favorite. I made these five models usi..
Clusters of Polyhedra Surrounding a Dodecahedron | RobertLovesPi.net
The cluster below is formed by augmenting each face of the dodecahedron above with an icosidodecahedron. Next, each triangular face is augmented with an icosahedron. Now every pentagonal face is augmented with a dodecahedron. Finally, the pentagonal faces of this cluster of polyhedra are augmented w..
The Icosidodecahedron, and Two Larger Polyhedra Made by Augmenting It | RobertLovesPi.net
Here's the icosidodecahedron -- one of the Archimedean solids. Next, here's what this solid looks like, if you augment each pentagonal face with a dodecahedron, and each triangular face with an icosahedron. Finally, here's what happens if you augment each pentagonal face of this secon..
A Zonohedron Based on the Faces, Edges, and Vertices of a Truncated Tetrahedron, as Well as Its Two-Fold Symmetry Axes, Its Three-Fold Symmetry Axes, and its X..
I made this polyhedron, which has 170 faces, using Stella 4d: Polyhedron Navigator. You may try this program, for free, at http://www.software3d.com/Stella.php.
The Octahemioctahedron, and Three Views of Its First Stellation | RobertLovesPi.net
This is the octahemioctahedron, which is one of the uniform polyhedra. It has twelve faces: eight equilateral triangles, and four regular hexagons. The hexagons pass through the center of this polyhedron. Here's the first stellation of this polyhedron, colored by face type. Here's a second..
The Great Dodecahemiicosahedron, With Two of Its Stellations | RobertLovesPi.net
Recently (here and here), I blogged about the small dodecahemiicosahedron, along with several of its stellations. Today, I got curious about it's "big brother," the great dodecahemiicosahedron, so I looked up the latter with Stella 4d (free trial download available here), examined som..
Some Pictures of the Partial Solar Eclipse | RobertLovesPi.net
This is how today's eclipse of the sun looked in Maumelle, Arkansas, USA, with solar viewing sunglasses held over my cell phone camera. The camera is set on maximum magnification (x10). Next, here's a shot of a shadow of a tree, along with another of the tree itself. Can you see the solar ..
More Stellations of the Small Dodecahemicosahedron | RobertLovesPi.net
In the last post here, I showed off the small dodecahemiicosahedron, along with three of its stellations. I've now had time to take a deeper dive into this stellation-series, and I found several more stellations to share. First, the 32nd stellation. Next, the 38th stellation. The 40th stellatio..
The Small Dodecahemicosahedron, and Three of Its Stellations | RobertLovesPi.net
Here's the small dodecahemicosahedron, which is one of the uniform polyhedra. It has 22 faces: the twelve star pentagons shown in red, and the ten regular hexagons shown in yellow. This solid has a long and interesting stellation-series. Three excerpts from that series are shown below. First, t..
A Pair of Symmetrohedra Derived From the Rhombicosidodecahedron | RobertLovesPi.net
To make this first symmetrohedron, I started with the rhombicosidodecahedron, augmented its thirty square faces with antiprisms, and then formed the convex hull of that solid. (I did all of this using Stella 34d: Polyhedron Navigator, which you can try for free right here.) The resulting polyhedra c..
Clusters of Rhombic Triacontahedra | RobertLovesPi.net
Here's a rhombic triacontahedron, possibly the most well-known of the Catalan solids. It's thirty faces are all golden rhombi (rhombi with their diagonals in the golden ratio). Here's what you get if you augment each face with another rhombic triacontahedron: Coloring this cluster-pol..
How to Lucid Dream | RobertLovesPi.net
Have you ever been dreaming, and actually knew you were dreaming? Did you get to have at least partial control over what happened in this dream? If so, that's lucid dreaming. If you've done it before, you can easily train yourself to do it again. If you haven't, this same exercise mig..
The Best Way to Lose a Spelling Bee | RobertLovesPi.net
In 4th grade, I finished in second place in my school district's spelling bee. This makes a much better story than winning, because of the word I could not spell correctly. That word was obeid (crap) obiedi (grrrr) obedei (blast it) obeedient that word that means you do as you are told. My moth..
Six Interpenetrating Regular Decagons | RobertLovesPi.net
To make the image above, using Stella 4d (available here), I started with a uniform polyhedron called the small icosihemidodecahedron, and then made the triangular faces of it invisible. Here's what this polyhedron looks like without its triangles hidden: The convex hull of either of these figu..
On Mental Health: My Reasons for Letting the Sunshine In | RobertLovesPi.net
There are quite a few posts on this blog on the subject of mental health, and they can be easily found by simply looking at that category, in the pull-down menu on the right side of your screen. In these posts, I have been quite candid about such things as my own panic disorder, PTSD,…
A Cluster of Fifteen Cuboctahedra | RobertLovesPi.net
There's one cuboctahedron in the center of this cluster, with each of its fourteen faces augmented by another cuboctahedron. The image below uses coloring of each face by its number of sides, while the next one is in "rainbow color mode." I made these images using Stella 4d, which you..
