#johnson solid

With the help of Tadeusz Dorozinski and Hunter Hughes, my new near-miss (the discovery of which was described here) is now better-understood. The isosceles triangles’ shared bases are 5% longer than the solid’s other edges, which is within the range generally allowed for near-misses. I have not yet found any mention of this discovery before I found it yesterday, while playing with a broken,…

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 noncoplanar. Instead of rhombi, therefore, I’m filling the gaps with pairs of isosceles triangles. I’m going to…