26 Apr
2006
26 Apr
'06
5:15 p.m.
Gareth wrote: << Rich Schroeppel wrote:
. . . Any triangle can be a hypoteface . . .
I thought of that too ... but is it true that "any triangle can be a hypoteface"? I think it only works for acute-angled ones. . . .
Definitely only works for acute triangles: Consider how a third plane can intersect a right dihedral angle. More generally the shape of an arbitrary right p-simplex (p-tetrahedron) is made by an affine hyperplane in R^p that intersects each positive coordinate axis. Again, the p-otenuse has one right corner at the origin of the posiive orthant, and the rest of them must be "p-acute" -- defined by requiring that each dihedral angle at the corner is acute. --Dan