I just realized this message was confusing. The png shows two _independent_ solutions to the no-face-uppermost problem for a seven and a five outcome die. E.g., number the faces of a heptagonal cylinder as in the upper picture and simply add the two uppermost. D&Devotees: Is this old? I assume the traditional solution is a tetradecahedral antiprism with the seven outcomes duplicated. --rwg On 2015-10-12 09:07, Bill Gosper wrote:
Odd barrel dice have the problem that two faces are always uppermost, so how do you label them? Alternative to face-transitivity, there are fair dice which cannot rest on any face, and yet have one face uppermost. Spoiler: gosper.org/5&7dice.png --rwg I assume these are old ideas. Check out Wikipedia if you haven't seen spherical, 6 outcome dice.