Additional References: Footnote 16: Sparteine has been used as a ligand for palladium-catalyzed allylic substitution reactions and olefin polymerization reactions. (a) Trost, B. M.; Dietsch, T. J. J. Amer. Chem. Soc. 1973, 95, 8200. (b) Togni, A.; Rihs, G.; Pregosin, P. S.; Ammann, C. Helv. Chim. Acta 1990, 73, 723. (c) Togni, A. Tetrahedron: Asymmetry 1991, 2, 683. (d) Pregosin, P. S.; Ruegger...

Three-dimensional counter-diffractometer data and a full-matrix least-squares method have been used to refine the crystal structure of a sub-silicic hastingsite in the space group C2/rn. The chemical composition of the amphibole is Na~.95K~.a~Cax.~4(Mg1.17Fe~+7Mn~.~4Ti~.39Fe~9A~.5~)Si5.2~A~2.~3~22.5~(~H)x.a4 with ceil parameters a = 9"8659(4), b = I8"OI39(8), c = 5'3545(2)-&, and fi = IO5O82(1)...

The asymptotics of the quantum $6j$ symbols corresponding to a hyperbolic tetrahedron is investigated and first two leading terms are determined for case that has an ideal or ultra-ideal vertex. These given by volume determinant Gram matrix tetrahedron.

Problems concerning complete structural characterization of quasicrystals involve locating the atomic positions as well as determining the distribution of elements at each site. Quasicrystalline approximants provide models for potential building units of quasicrystals, but a clear determination of the elemental decorations in such approximants also remains incomplete. We report experimental and...

A lattice tetrahedron T ⊂ R3 is a tetrahedron whose four vertices are all in the lattice Z3. Lattice tetrahedra are preserved by those affine linear maps of the form ~v 7→ A~v +~b, such that A is an element of GL(3,Z) and ~b is an element of the lattice Z3. Such affine linear maps are called unimodular maps. We say that a lattice tetrahedron whose barycentre is its only non-vertex lattice point...

We present a procedure for bisecting a tetrahedron T successively into an infinite sequence of tetrahedral meshes ¡Tü , ZTX , ST1, ... , which has the following properties: (1) Each mesh !Tn is conforming. (2) There are a finite number of classes of similar tetrahedra in all the ¿Tn , n > 0. (3) For any tetrahedron T? in ¿T" , n(T") > cxn(T), where n is a tetrahedron shape measure and cx is a c...

The 8-tetrahedra longest-edge (8T-LE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longest-edge. The associated local refinement algorithm can be described in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint tetrahedron bisection procedure. An effecti...

In order to investigate the displacement of the IO4 tetrahedron in the ferroelectric phase II of pyridinium periodate in detail, we performed X-ray structural analysis with the use of the estimated site occupancies of carbon and nitrogen atoms at many temperatures. We confirmed the continuous increase of the rotation angle of the IO4 tetrahedron about the a-axis with decreasing temperature in t...