Adam, Perusing your lovely math blog once again, I noticed your Nov. 10, 2014 post about a new holyhedron with only 12 sides. At first I was very excited, and also amazed he got it so low. Then I read his description of his examples. The problem is, they are not holyhedra. As Conway described the problem to math-fun (as far as I know, this was the first place he publicly mentioned it), a holyhedron is a polyhedron in 3-space that is a connected component of the boundary of a 3-manifold, each of whose faces is not simply connected. More specifically, Conway defined it as a boundary component of a "Boolean compound of finitely many closed half-spaces" — if I remember his wording — each of whose faces, etc. It *certainly* must be a topological 2-manifold, unlike Nathan Ho's examples. But I will need to be reminded how to access the math-fun archives, and check to be sure of his exact words. (I also thought I played some role in the coining of the word "holyhedron" — which I remember Conway felt might offend some religious folk unless an E were added to make "holeyhedron". But again, checking the archives will clarify my somewhat foggy memory about the details of what happened lo those 17 years ago.) Regards, Dan