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A single 30-tetrahedron ring Boerdijk–Coxeter helix within the 600-cell, seen in stereographic projection. Regular tetrahedra can be stacked face-to-face in a chiral aperiodic chain called the Boerdijk–Coxeter helix.
In this motif, the two tetrahedra share a common edge. The inorganic polymer silicon disulfide features an infinite chain of edge-shared tetrahedra. In a completely saturated hydrocarbon system, bitetrahedral molecule C 8 H 6 has been proposed as a candidate for the molecule with the shortest possible carbon-carbon single bond. [5]
A Boerdijk helical sphere packing has each sphere centered at a vertex of the Coxeter helix. Each sphere is in contact with 6 neighboring spheres. The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and Arie Hendrick Boerdijk [], is a linear stacking of regular tetrahedra, arranged so that the edges of the complex that belong to only one tetrahedron form three intertwined helices.
This configuration, like Möbius, can also be represented as two tetrahedra, mutually inscribed and circumscribed: in the integer representation the tetrahedra can be 0347 and 1256. However, these two S 4 configurations are non-isomorphic, since Möbius has four pairs of disjoint planes, while the latter one has no disjoint planes. For a ...
n, the anion is a tridimensional network of tetrahedra in which all oxygen corners are shared. If all tetrahedra had silicon centers, the anion would be just neutral silica [SiO 2] n. Replacement of one in every four silicon atoms by an aluminum atom results in the anion [AlSi 3 O − 8] n, whose charge is neutralized by the potassium cations K +.
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In single-chain silicates, which are a type of inosilicate, tetrahedra link to form a chain by sharing two oxygen atoms each. A common mineral in this group is pyroxene . Double chain tetrahedra.
Tetrahedral packaging. Aristotle claimed that tetrahedra could fill space completely. [4] [5]In 2006, Conway and Torquato showed that a packing fraction about 72% can be obtained by constructing a non-Bravais lattice packing of tetrahedra (with multiple particles with generally different orientations per repeating unit), and thus they showed that the best tetrahedron packing cannot be a ...