Apologies: I had completely forgotten that the Meissner construction replaces only _three_ of the six edges. So yes, you (and he) are correct: it does have constant width, but not tetrahedral symmetry. The sectional curve along each edge which would achieve full symmetry must lie somewhere between the single circular arc used by Meissner, and the pair of arcs resulting from continuation of the spherical caps over the faces ("Releaux"). It's surprising that nobody seems to have explicitly given an analytical form for either implicitly or parametrically. Fred Lunnon On 1/10/13, Dan Asimov <dasimov@earthlink.net> wrote:
P.S. Here's a nice write-up about the Meissner tetrahedron: (published in Math Intelligencer v.33 no.3 2011:
<http://www.mi.uni-koeln.de/mi/Forschung/Kawohl/kawohl/pub100.pdf>
--Dan
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