I would certainly like to see such an encyclopedia. And here's a problem: is there a nice triangle center (in the plane of the triangle) whose definition depends on a 3-dim configuration, in the sense that the 3-dim definition is "more natural" than any plane definition? Clark Kimberling -----Original Message----- From: Henry Baker [mailto:hbaker1@pipeline.com] Sent: Thursday, November 03, 2011 8:46 AM To: math-fun Cc: Kimberling, Clark Subject: Re: [math-fun] Tetrahedral altitudes [This question is probably aimed at Clark Kimberling.] I liked the little table at the beginning of this paper about which triangle thingy's generalized to 3-space and n-space. Is there a more encyclopedic version of this table, together with all the proofs? One of the most common questions by (insightful) high school geometry students is "what happens to this thingy in 3-space?". Also, the computation of such objects in higher spaces becomes more & more involved (as the computer graphics community knows all too well). Hopefully, such an encyclopedia would include some of these computational formulae. It would be nice to know where to point. At 09:14 PM 11/2/2011, Fred lunnon wrote:

See http://www.geometrie.tuwien.ac.at/havlicek/pub/hoehen.pdf Hans Havlicek, Gunter Weiß "Altitudes of a Tetrahedron and Traceless Quadratic Forms" Tech. Univ. Vienna (no date?)