naa a22 4500 510736882 CHVBK 20180411083013.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s13366-011-0079-x doi (NATIONALLICENCE)springer-10.1007/s13366-011-0079-x The kinematics of a framework presented by H. Harborth and M. Möller [Elektronische Daten] [P. Fazekas, O. Röschel, B. Servatius] We consider a model of interlinked tetrahedra which has been described by Harborth and Möller (Geombinatorics XVII(2):53-56, 2007). It consists of 16 congruent regular tetrahedra connected via 32 spherical joints (in the vertices of the tetrahedra). In this arrangement they define a saturated packing. Every vertex of a tetrahedron is linked to a vertex of another tetrahedron. As the classical Grübler-Kutzbach-Chebyshev formula gives a theoretical degree of freedom f=−6 for this kinematic chain, the model is supposed to be rigid. However, we can demonstrate that this mechanism still admits at least a two-parametric self-motion in the general position. Further on we consider a special, degenerate case of this model, which again admits a two-parametric self-motion. This motion contains geometrically interesting positions regarding the cross-section of possible prismatic channels through the model. These channels occur as empty space through the model if the tetrahedra are considered to be solid bodies. We present positions with vanishing channels and with a cross section of area a 2=1 for tetrahedra with edge length a :=1. The Managing Editors, 2011 Saturated packings of regular tetrahedra nationallicence Overconstrained mechanisms nationallicence Zeolite-models nationallicence Flexibility of packings nationallicence Fazekas P. Institute for Geometry, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria aut Röschel O. Institute for Geometry, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria aut Servatius B. Institute for Geometry, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria aut Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 201-209 0138-4821 54:1<201 2013 54 13366 https://doi.org/10.1007/s13366-011-0079-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-011-0079-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fazekas P. Institute for Geometry, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria aut NATIONALLICENCE 700 1- Röschel O. Institute for Geometry, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria aut NATIONALLICENCE 700 1- Servatius B. Institute for Geometry, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 201-209 0138-4821 54:1<201 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer