10 Oct
2003
10 Oct
'03
1:24 p.m.
On Fri, 10 Oct 2003 asimovd@aol.com wrote:
I have the impression that the Poincaré dodecahedral manifold D created by a 1/10 rotation identifying opposite faces, and the one using a -1/10 rotation, are isometric to each other -- much as a right- and a left-handed H opf fibration of the 3-sphere are isometric.
Yes of course they're isometric, but only by an orientation-reversing isometry.
What I'm wondering now is whether D double-covers a non-orientable manifold.
I already answered this in the negative. The group is both metachiral and parachiral, the latter meaning that it is not the chiral part of an achiral group. John Conway