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I know how to calculate the polyhedral packing fraction of simple crystal structures, but in a lot cases, the structure is not cubic and the polyhedra are irregular, and it becomes very tedious to calculate the polyhedral packing fractions by hand. I am wondering if anyone knows of any software that can calculate the polyhedral packing fractions based on an input structure file(i.e., a .cif file)?

For example, for some common oxides: NiO consists of densely packed octahedra, while ZnO consists of tetrahedra connected only by point-sharing (not densely packed). The polyhedral packing fraction of the former is much higher than that of the latter: enter image description here enter image description here

ADDENDUM for non crystallographers:

enter image description here

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    $\begingroup$ I can get results from google looking for 'packing fraction' but no hits for'polyhedral packing fraction' $\endgroup$
    – pippo1980
    Commented Nov 26 at 22:21
  • $\begingroup$ Same, which I find quite odd given that the concept's easily derivative of the typical 'atomic packing fraction'. $\endgroup$
    – rmza7
    Commented Nov 27 at 17:07
  • $\begingroup$ WIKIPERDIA Packing fraction may refer to: Packing density, the fraction of the space filled by objects comprising the packing Atomic packing factor, the fraction of volume in a crystal structure that is occupied by the constituent particles Packing fraction (mass spectrometry), the atomic mass defect per nucleon $\endgroup$
    – pippo1980
    Commented Nov 27 at 18:08
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    $\begingroup$ Platon ?? VOID & SOLV Calculations ?? $\endgroup$
    – pippo1980
    Commented Nov 27 at 21:46
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    $\begingroup$ So with polyhedral you dont mean the shape of the crystals base unit but that you want to evaluate only the volume occupied by your depicted gray volume without taking into account the entire VdW radii of the red atoms ?? $\endgroup$
    – pippo1980
    Commented Nov 28 at 8:44

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