I was just performing a Google search on “uniform polyhedron,” as I’m sure we all have on occasion while no one is looking. I must admit that I hadn’t realized that these little scamps may be regular (if also face and edge transitive), quasi-regular (if edge transitive but not face transitive), or semi-regular (if neither edge nor face transitive). It had also never struck me that the faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra (I’m sure that you are as flabbergasted as me to learn this). All I can say is that I ran across this Wikipedia page and found much more than I bargained for. Silly me. It turned out that what I was really looking for was the Platonic solids, which are regular, convex polyhedra (or polyhedrons) that are constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. There are only five solids that meet all these criteria: the tetrahedron (four triangular faces), the cube (six square faces), the octahedron (eight triangular faces), the dodecahedron (twelve pentagonal, or five-sided, faces), and the icosahedron (twenty triangular faces). It turned out it was the icosahedron (plural icosahedra or icosahedrons) that I was looking for. The reason for my interest is that I just saw a mega-cool project on the hackaday.io website. As we see from this video, the project’s creators have constructed an icosahedron covered in flashing LEDs.  
As I always say: “Show me a LED flashing, and I’ll show you a man drooling.” First, you can display images on this little beauty. Second, it’s equipped with an attitude sensor, which allows the images to be stabilized so they don’t appear to move when the icosahedron is rotated. Now, this is pretty tasty, but do you remember my Awesome Audio-Reactive Artifact project? As you might recall, I started by taking a small faux antique suitcase and adding some defunct vacuum tubes.  
I also attached a bunch of tri-colored LEDs to the bottom of the tubes. Then I used a microphone breakout board (BOB), a MSGEQ7 audio spectrum analyzer chip, and an Arduino to transform this little beauty into an audio-reactive display. Well, I was just idly wondering how I would go about adding audio-reactive capabilities to a LED-covered icosahedron (i.e., how would you display the different frequencies colors to best effect), not that I have one… yet. What say you? Could you be tempted to build one of these little rascals?