From meister@gaak.lcs.mit.edu Mon Sep 9 00:48:52 1991 Return-Path: Received: from gaak.LCS.MIT.EDU by life.ai.mit.edu (4.1/AI-4.10) id AA26612; Mon, 9 Sep 91 00:48:52 EDT Received: by gaak.LCS.MIT.EDU id AA06357; Mon, 9 Sep 91 00:48:09 EDT Date: Mon, 9 Sep 91 00:48:09 EDT From: meister@gaak.lcs.mit.edu (phil servita) Message-Id: <9109090448.AA06357@gaak.LCS.MIT.EDU> To: cube-lovers@ai.mit.edu Subject: Square One "Square One" is also available at Games People Play in Cambridge, Mass. I just purchased one a few days ago. It turned out to be more interesting than i had expected. The puzzle is comprised (essentially) of two halves of 8 pieces each, 4 corners, and 4 'edges'. All pieces radiate outward from the center. The 'edge' pieces expand outward at a 30 degree angle, while the corners expand outward at a 60 degree angle. The center layer is composed of just 2 pieces. If you removed the top slice, the center slices would trace out quadrilaterals ABIK and BDJL (or ACIJ and BDKL, etc) below. The center slice serves no major function save as a "gate" which allows or disallows rotation about one of the skewed axes formed by the two slices. To rotate about some axis you must line up the "gate" with the axis. While it is possible to swap the center pieces with respect to the corners frame of reference, doing so is really of no importance to the "meat" of the puzzle. Top View: (in lousy ascii resolution) A B C D -------------*-------------*-------------- | * * | | * * | | * * | E * * * * F | * * * * | | * * * * | | * O | | * * * * | | * * * * | G * * * * H | * * | | * * | | * * | -------------*-------------*-------------- I J K L Side View: _____________________ | | | | |______|_____|______| top | | | |______|____________| center "gate" lined up for left axis | | | | |______|_____|______| bottom All meaningful moves either rotate the top or bottom face, line up the center gate with some skew axis, or twist about a skew axis 180 degrees. The neat thing about the puzzle is that moves do not necessarily preserve the cube shape of the puzzle, or even the number of corner/edge pieces that are on each side. It is possible, for instance, to have only 3 corners on the top face, and 6 edges, while 5 corners and 2 edges are on the bottom face. A notation for this beast is somewhat cumbersome. If anyone wants, I will try to describe what i am using. After playing with it for a few hours, i *thought* i had mapped out a complete solution algorithm; however i was later playing with the wierd shapes you could put the puzzle into, and eventually started putting it back to "Square One", and was very surprised to end up in a position with just 2 of the edges swapped! Since this puzzle acts much like the Skewb, each move essentially cutting the puzzle in half (ignoring the gate layer), i did not expect this to be possible. It took a bit of thought before the light hit, and i went on to construct a crude "Parity Swap" transform. Currently the best one i have found cycles around UF -> UL -> UB -> UR, and takes 28 'moves'. (a 'move' being defined as any motion of some slice, regardless of degrees turned) Anyone else found anything better? Square One is one of the better variations on the cube theme i have seen in a long time. Find one and have fun. -phil