Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site decwrl.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!decwrl!dec-rhea!dec-jon!moroney From: moroney@jon.DEC Newsgroups: net.math Subject: Re: Polyhedral dice Message-ID: <3702@decwrl.UUCP> Date: Fri, 21-Sep-84 14:41:46 EDT Article-I.D.: decwrl.3702 Posted: Fri Sep 21 14:41:46 1984 Date-Received: Tue, 25-Sep-84 21:52:03 EDT Sender: daemon@decwrl.UUCP Organization: DEC Engineering Network Lines: 29 >> However, fair dice can be made as long as all the FACES are identical >> to each other, although they may not be regular polygons. The vertices >> ......... >The requirements are more stringent than that, and here's a counter >example of an unfair die, of uniform material, all faces equal. >Start with an octohedron. Grab it by two opposing vertices >and pull it apart and give it a half twist. Now connect each >of the vertices along the rift to the two closest ones in the other >half. I find it hard to draw slanty lines in text. >This results in 8 new equilateral triangles connecting the old >square bases of the pyramidal caps. >Do this same process again. .......the likelihood that this die land on one of the original triangles is exceedingly small... You are right.. There is another important requirement - the angle between any 2 faces must be the same, or each face must have an identical environment around it to all the other faces. So far the only polyhedra which meet these that I know of are the 5 regular polyhedra, the "30" in role-playing games (Anyone know the official name for this?) and the 12-sided rhomboid I mentioned earlier. Mike Moroney ..!decvax!decwrl!rhea!jon!moroney