Shapes of centrally symmetric octahedra with prescribed cone-deficits

The space of Euclidean cone metrics on centrically symmetric octahedra with fixed cone angles θi < 2π, with total surface area 1, has a natural hyperbolic metric, and is locally isometric to hyperbolic 3-space. The metric completion of the space is isometric to a hyperbolic ideal tetrahedron whose dihedral angles are half the cone-deficits 2π − θi.

Crystal structure of dibenzyldimethylsilane

In the title compound, C16H20Si, a geometry different from an ideal tetrahedron can be observed at the Si atom. The bonds from Si to the benzylic C atoms [Si—C = 1.884 (1) and 1.883 (1) Å] are slightly elongated compared to the Si—Cmethylbonds [Si—C = 1.856 (1) and 1.853 (1) Å]. The Cbenzyl—Si—Cbenzylbond angle [C—Si—C = 107.60 (6)°] is decreased from the ideal tetrahedral angle by 1.9°. These distortions can be explained easily by Bent's rule. In the crystal, molecules interact only by van der Waals forces.

Distortions in tetrahedral copper(I)–phosphine complexes: bis(triphenylphosphine)copper(I) nitrate

The crystal structure of bis(triphenylphosphine)copper(I) nitrate has been determined by a three-dimensional X-ray diffraction study. The copper(I) atom is bonded to the two phosphines and two oxygen atoms of the nitrate group. However, the molecule is distorted from that of an ideal tetrahedron, with the P—Cu—P angle being 131.1°.