The Kinematics of a Framework Presented by H. HARBORTH and M. MÖLLER

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.