On the Tetrahedroid as a particular case of the 16-nodal quartic surface.
We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of . As a result we prove that for any even dimension there exists a unique compact arithmetic hyperbolic -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...
Bz the quadrileteral condition in a given net there is meant the following implication: If are arbitrary points, no three of them lie on the same line, with coll (collinearity) for any five from six couples then there follows the collinearity coll for the remaining couple . In the article there is proved the every net satisfying the preceding configuration condition is necessarity the Ostrom net (i.e., the net over a field). Conversely, every Ostrom net satisfies the above configuration...