Richard's paper mentions mentions that the 4 altitude lines of a tetrahedron, through vertices and perpendicular to faces, do not necessarily concur in a common point. A long time ago I came across a charmingly antiquated tome: Nathan Altshiller-Court "Modern pure solid geometry" (1935) which I seem to remember stated the theorem that the altitudes always lie on a quadric; though his notation --- undefined --- for this property was something confusingly obscure. There were several other theorems of a similar nature. Can anybody confirm this? Has any further work in this direction taken place more recently? WFL On 10/29/11, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
... I've just submitted a paper, ``Five-point circles, the 76-point sphere, and the Pavillet tetrahedron'' to the Monthly. The theme is that triangle geometry is not dead. I would attach a copy if attachments were allowed; I will entertain individual requests. ...