Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedron–vertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded as four vertex-references for each tetrahedron, which requires 128m bits where m is the number of tetrahedra in the mesh. Our ‘Grow & Fold’ format red...

A new formula for the volume of a hyperbolic and spherical tetrahedron is obtained from the quantum 6j-symbol. This formula is of symmetric form with respect to the symmetry of the tetrahedron.

1 Abstract Standard representations of irregular nite element meshes combine vertex data sample coordinates and node values and connectivity tetrahedron-vertex incidence. Connectivity speciies how the samples should be interpolated. It may beencoded for each tetrahedron as four vertex-references,

The problem of equimomental systems a rigid body is considered. It shown that the system four equal masses located at vertices an isosceles tetrahedron to given body. A material points tetrahedron, which cometary nuclei 67P Churyumov-Gerasimenko, has been constructed.

A triangulation of a 3-manifold can be shown to be homeomorphic to the 3-sphere by describing a discrete Morse function on it with only two critical faces, that is, a sequence of elementary collapses from the triangulation with one tetrahedron removed down to a single vertex. Unfortunately, deciding whether such a sequence exist is believed to be very difficult in general. In this article we pr...

Despite the rarity, large negative linear compressibility (NLC) was observed in metal-organic framework material Zn(HO3PC4H8PO3H)∙2H2O (ZAG-4) in experiment. We find a unique NLC mechanism in ZAG-4 based on first-principle calculations. The key component to realize its large NLC is the deformation of H3O(+) tetrahedron. With pressure increase, the oxygen apex approaches and then is inserted int...

The bridging ligands L(1) and L(2) contain two N,N-bidentate pyrazolyl-pyridine units linked to a central aromatic spacer unit (1,2-phenyl or 2,3-naphthyl, respectively). Reaction with Ni(II) salts and treatment with the anions tetrafluoroborate or perchlorate result in formation of dinuclear complexes having a 2:3 metal:ligand ratio, with one bridging and two terminal tetradentate ligands. In ...

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...