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- W4387156700 abstract "We intend to continue our previous papers (cite{MSz17} and cite{MSz18}, as indicated there) on dense ball packing hyperbolic space $HYP$ by equal balls, but here with centres belonging to different orbits of the fundamental group $Cw(2z, 3 le z in bN$, odd number), of our new series of {it tube or cobweb manifolds} $Cw = HYP/BCw$ with $z$-rotational symmetry. As we know, $BCw$ is a fixed-point-free isometry group, acting on $HYP$ discontinuously with appropriate tricky fundamental domain $Cw$, so that every point has a ball-like neighbourhood in the usual factor-topology. Our every $Cw(2z)$ is minimal, i.e. does not cover regularly a smaller manifold. It can be derived by its general symmetry group $BW(u, v, w = u)$ that is a complete Coxeter orthoscheme reflection group, extended by the half-turn $Bh$ $(0 leftrightarrow 3, 1 leftrightarrow 2)$ of the complete orthoscheme $A_0A_1A_2A_3 sim b_0b_1b_2b_3$ (Fig.~1). The vertices $A_0$ and $A_3$ are outer points of the $HYP$, as $1/u + 1/v le 1/2$ is required, $3 le u = w, v$ for the above orthoscheme parameters. The situation is described first in Figure 1 of the half trunc-orthoscheme $W$ and its usual extended Coxeter diagram, moreover, by the scalar product matrix $(b^{ij}) = (langle Bb^i, Bb^j rangle)$ in formula (1.1) and its inverse $(A_{jk}) = (langle BA_j, BA_k rangle)$ in (1.3). These will describe the hyperbolic angle and distance metric of the half trunc-orthoscheme $W$, then its ball packings, densities, then those of the manifolds $Cw(2z)$. As first results we concentrate only on particular constructions by computer for probable material model realizations, atoms or molekules by equal balls, for general $W(u;v;w=u)$ as well, summarized at the end of our paper." @default.
- W4387156700 created "2023-09-30" @default.
- W4387156700 creator A5029006855 @default.
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- W4387156700 date "2023-09-26" @default.
- W4387156700 modified "2023-10-18" @default.
- W4387156700 title "Dense ball packings by tube manifolds as new models for hyperbolic crystallography" @default.
- W4387156700 doi "https://doi.org/10.48550/arxiv.2309.15168" @default.
- W4387156700 hasPublicationYear "2023" @default.
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