From dik@cwi.nl Sat Oct 21 22:52:22 1995 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA21513; Sat, 21 Oct 95 22:52:22 EDT Received: from bever.cwi.nl by charon.cwi.nl with SMTP id ; Sun, 22 Oct 1995 03:52:11 +0100 Received: by bever.cwi.nl id ; Sun, 22 Oct 1995 03:52:12 +0100 Date: Sun, 22 Oct 1995 03:52:12 +0100 From: Dik.Winter@cwi.nl Message-Id: <9510220252.AA04563=dik@bever.cwi.nl> To: cube-lovers@life.ai.mit.edu Subject: Re: Spotty Megaminx Content-Length: 1116 > I've never seen anything on patterns for the megaminx, with the > sole exception of Kurt Endl's book "Megaminx". It is long ago I had it in my hands, and I have no books. What I say is from memory; probably correct. Note that a face turn induces an even permutation on both the corner and the edge "cubies". So odd permutations are not possible. On the other hand (if I remember well) *all* combinations of even permutations are possible. > There are 6 opposite pairs of faces on the megaminx. There are 4 ways > to rotate the centres for each pair to generate a 10 spot. I'll > speculate that there are 6*4 = 24 possible 10-spots. Right. > I suspect various 12-spots are possible. I have no idea how to > easily permute centre pieces on the megaminx. Indeed. Every rotation of the center skeleton is possible (if you consider the remainder fixed...). So there are 12 centers that can come out at top; for each center at top you have 5 possible positions of the remainder leading to 60 configurations. Of these 24 are 10-spots, 1 is the solved puzzle, so the remainder (35) is 12-spots. dik