X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,aed89f7a2fcf37e8 X-Google-Attributes: gidf996b,public From: ecclesia@delenda.est (Frank Newhouse) Subject: Re: HyperCube (Diamond Explained) Date: 1997/06/11 Message-ID: <339f06b2.75490770@news.idecnet.com>#1/1 X-Deja-AN: 248218319 References: <339D4F82.1296@garnet.fsu.edu> <339E05CD.5CA6@garnet.fsu.edu> Organization: Unisource Espana NEWS SERVER Newsgroups: alt.ascii-art On Wed, 11 Jun 1997 18:48:45 +0100, salesman wrote: >>I think these figures are right (I never tried to counts edges and faces >>of a hypercube before!) >> >> Dimensions Vertices Edges Faces >>Point 0 1? >>Segment 1 2 1 >>Square 2 4 4 1 >>Cube 3 8 12 6 >>H-cube 4 16 30 18 Your explanations and drawings are quite good, but -sorry to tell you- your figures are wrong The tesseract, or hypercube, has -4 dimensions, -16 vertices -OK so far-, - 32 edges, not 30 (not too hard to see; you have 12 edges in the cube you begin with, another 12 edges in the cube you end with, and eight edges connecting each vertex in the first cube with its homologue in the second cube) -24 faces, not 18 (again, 6 faces in cube 1 plus 6 faces in cube 2, plus 12 faces connecting each edge of cube 1 with its homologue in cube 2) -and last but not least, 8 cubical "faces" (cube 1, cube 2, and 6 cubes connecting each face of cube 1 with its homologue in cube 2)