Jammed frictional tetrahedra are hyperstatic

We prepare packings of frictional tetrahedra with volume fractions $\phi$ ranging from 0.469 to 0.622 using three different experimental protocols under isobaric conditions. Analysis via X-ray micro-tomography reveals that the contact number Z grows with $\phi$, but does depend on the preparation protocol. While there exist four different types of contacts in tetrahedra packings, our analysis shows that the edge-to-face contacts contribute about 50\% of the total increase in Z. The number of constraints per particle C increases also with $\phi$ and even the loosest packings are strongly hyperstatic i.e. mechanically over-determined with C approximately twice the degrees of freedom each particle possesses.