Talk:Regular Polytopes (book)

message: Siobhan Roberts' biography quotes Sir Harry Kroto, codiscoverer of fullerenes: "I knew Buckminster Fuller's work, but I didn't know the Coxeter connection.  Certainly, Coxeter's book Regular Polytopes would have been helpful."  If there's anything in Regular Polytopes about the truncated icosahedron, let alone the higher Goldberg polyhedra, I can't find it!  —Tamfang 01:45, 16 April 2007 (UTC)
thread_title:  fullerenes 

message: It praises the book too much. Not enough citations for all the circlejerking.  — Preceding unsigned comment added by 96.231.116.47 (talk) 15:48, 29 September 2012 (UTC)
thread_title: Reads like an advertisement

message: The stereographic {5,3,3} from Jenn3d is not the most appropriate choice.  This is a representation of a curved object, a tiling of S3 (positively-curved 3-space); Regular Polytopes is about objects with flat boundaries in flat 4-space.  While conflating the two is a convenient way to visualize the convex 4-polytopes, I think Coxeter would object.  Better a flat projection.  —Tamfang 05:23, 2 July 2007 (UTC)
replies: text: I've changed the image and tweaked the caption. Actually, both images are projections of the 120-cell into 3-space, so the underlying object is the same - the difference is that one projection preserves angles, the other preserves straight lines. Gandalf61 08:40, 2 July 2007 (UTC)
replies: text:  Good change. Maybe a lores photographed book cover would be nice too? (I have a paperback copy at least). Tom Ruen 16:26, 2 July 2007 (UTC)
replies: text:  I found my mislaid new copy!  —Tamfang 18:11, 20 August 2007 (UTC)

text:  The Jenn figure can be seen as the result of two projections – a gnomonic projection from E4 to the S3, followed by a stereographic projection from S3 to E3 – but what angles does it preserve?  The angle between edges is 108° (the pentagonal angle) in the polychoron, 109.5° (the tetrahedral angle) in the projection; the angle between faces is 116.6° in the polychoron, 120° in the projection; the angle between cells is 144° in the polychoron, 180° in the projection.  (Naturally I'm getting some of these figures from Coxeter's table!)  —Tamfang 06:16, 5 July 2007 (UTC)
replies: text: Tamfang, that must be a rhetorical question, as you seem to know the answer already. If you don't like the new illustration then find your own. I tried to help out, and you just produce more complaints. I can't read your mind to work out what you want here, so I am done. Gandalf61 10:07, 5 July 2007 (UTC)
replies: text:  Did I say I'm unhappy with the new picture??  Au contraire!  I'm asking for clarification of something you said about the old one, if that's not too much trouble.  —Tamfang 05:17, 6 July 2007 (UTC)

text:  I'm interested in the topic, mostly since I've been annoyed how best to explain/label what the diagrams are. I'd call the Jenn curved diagrams as uniform 3-sphere surface tessellations, viewed by stereographic projection from 4-space into 3-space. ANYWAY to Tamfang's question (maybe), I see the curved projection is preserving angles from the 3-sphere surface tessellation, not the 4-space regular polytope. (Sometime I'd like to get some regular polyhedron stereographic projections, curved and linear edges for comparsion as well.) Tom Ruen 17:23, 5 July 2007 (UTC)
replies: text:  That's how I see it too.  —Tamfang 05:17, 6 July 2007 (UTC)
thread_title:  the illo