Message #3664

Subject: Re: [MC4D] Stellated intersection of cylinders
Date: Tue, 21 Feb 2017 05:33:20 +0000

First of all, it’s my bad that I double posted. Replies don’t go to the same thread.

I also guess the two views are equivalent here. I don’t have a real proof. I agree that the union of intersections of subsets is easier to deal with. The stellation view has a better connection to normal flat polyhedra.

Actually, you can view a regular dodecahedron as the intersection of 12 half spaces defined by the 12 faces. Then the small stellated dodecahedron can be viewed as the union of 12 pentagonal cones, each of which is the intersection of 5 half spaces. So my intuition is that the stellation view and the union of intersections view are equivalent.

I chatted with Alexandr in the mf8 forum:

He said "As far as I know. I was the first who built all possible variants ten cylinder. What I presented are here, it’s not all variants. I chose the most interesting for me." and although he showed pictures of 11 variants for the ten cylinder case, there are 14 symmetrical variants altogether.