From cube-lovers-errors@mc.lcs.mit.edu Sun Apr 5 16:13:15 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id QAA20772; Sun, 5 Apr 1998 16:13:15 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Mon Mar 30 20:40:51 1998 Date: Mon, 30 Mar 1998 20:41:13 -0400 (EDT) From: Jerry Bryan Subject: Pretty vs. Not-So-Pretty Isoglyphs To: Cube-Lovers Message-Id: After looking at a lot of isoglyphs and partial isoglyphs in the last little while, I wonder if it's not the case that some of the non-continuous isoglyphs are prettier than some of the continuous ones, and that some of the partial isoglyphs are prettier than some of the isoglyphs? Continuous isoglyphs do *in general* seem prettier than non-continuous ones, and isoglyphs do *in general* seem prettier than partial isoglyphs. But consider the following two (counter?) examples. The glyph 000 XXX 000 yields (among other things) L2 F2 L2 R2 F2 R2, which is a non-continuous partial isoglyph. It looks about as follows (quite pretty and striking, in my opinion): XXX XXX XXX 0X0 0X0 0X0 0X0 0X0 0X0 0X0 0X0 0X0 0X0 0X0 0X0 XXX XXX XXX On the other hand, U B2 R2 F2 L2 U L2 F2 U2 R' B' R F' L' U2 B2 R2 B' D' U' is a real mess in my opinion, even though it is a continuous isoglyph. It looks something like the following. X00 0X0 XXX XOX XXX X00 00X XX0 0X0 0X0 0XX X00 00X XXX X0X 00X 0XX X0X Notice that the partial isoglyph which was my first example "looks" fairly continuous, even though it really isn't. The reason it looks that way is that it is continuous along all the edges where the non-solid glyphs come together. Call such a non-continuous partial isoglyph quasi-continuous. I think your eye tends to ignore the solid faces anyway, so that a quasi-continuous partial isoglyph tends to be very striking and very pretty. For example, there are a number of 4-H and 4-T patterns among the partial isoglyphs which are quasi-continuous and which are very pretty. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990