In this paper we propose a method to obtain a tetrahedral model of the human head by labeling elements of a tetrahedral mesh. To work with meshes as regular as possible, we use the notion of Almost Regular Tesselation (ART) providing tetrahedral meshes with good quality elements. The proposed labeling method uses segmented M.R.I. containing main tissues of the head as input. The labeling is don...

Water defines life on Earth from the cellular to the terrestrial level. Yet the molecular level arrangement in water is not well understood, posing problems in comprehending its very special chemical, physical and biological properties. Here we present high-resolution x-ray diffraction data for water clearly showing that its molecular arrangement exhibits specific correlations that are consiste...

A peptide derived from Aβ17-36 crystallizes to form trimers that further associate to form higher-order oligomers. The trimers consist of three highly twisted β-hairpins in a triangular arrangement. Two trimers associate face-to-face in the crystal lattice to form a hexamer; four trimers in a tetrahedral arrangement about a central cavity form a dodecamer. These structures provide a working mod...

In the structure of the title triorganophosphine oxide, C16H19OP, the P-O bond is 1.490 (1) Å. The P atom has a distorted tetrahedral geometry. The O atom inter-acts with both phenyl groups of a neighboring mol-ecule [C⋯O = 2.930 (3) and 2.928 (4) Å]. The C-O interaction directs an extended supramolecular arrangement along the a-axis.

Four cubic compounds are reported that contain the supertetrahedral cluster [M(4)Sn(4)S(17)](10)(-) where M = Mn, Fe, Co, Zn. The cluster features a central quadruply bridging sulfide ion (mu(4)-S) that holds together four divalent M atoms in a tetrahedral arrangement. This core is capped with four tridentate [SnS(4)](4)(-) fragments to complete the structure.

The tetrameric macrocycle [(P(mu-NtBu))2(1,4-(NH)2C6H4)]4, obtained from the reaction of the phosphazane dimer [ClP(mu-NtBu)]2 with p-phenylenediamine, has an unusual folded conformation in the solid state and contains a roughly tetrahedral arrangement of endo N-H groups for the potential coordination of anions.

A new effective pair potential model is proposed for computer simulations of liquid methylene fluoride and used in Monte Carlo simulations on the isothermal-isobaric ensemble at two different temperatures. The new model is able to reproduce the thermodynamic ~internal energy, density, heat capacity, vapor-liquid equilibrium! and structural ~neutron diffraction data! properties of liquid methyle...

We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. (This shows the “Strong Dirac” conjecture to be false for pseudolines.) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classe...

Among the many ways to view oriented matroids as geometrical objects, we consider two that have special properties: • Bland’s analysis of complementary subspaces in IRn [2] has the special feature that it simultaneously and symmetrically represents a realizable oriented matroid and its dual; • Lawrence’s topological representation of oriented matroids by arrangements of pseudospheres [4] has th...