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Is the classification of space-filling (by identical copies) convex polyhedra in R^3 is known ?

There are only 5 "parallelohedra" - filling by translation. But if relax that property to identical (but not necessary by parallel translation), there are more as Wikipedia suggests. But it is not clear is the list described there is final or not.

To be precise I am asking about honeycombs filling the space by copies of single polyhedron, not several of them, as it happens, for example in famous Weaire–Phelan structure.

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    $\begingroup$ I remember working, unsuccessfully, under John Conway on space-filling tetrahedra in 1975. Michael Goldberg, Three infinite families of tetrahedral space-fillers, Journal of Combinatorial Theory, Series A Volume 16, Issue 3, May 1974, Pages 348-354 sciencedirect.com/science/article/pii/0097316574900582 was probably state-of-the-art at the time. $\endgroup$
    – Gerry Myerson
    Commented Jun 22, 2020 at 7:29
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    $\begingroup$ See also Marjorie Senechal, Which Tetrahedra Fill Space? Mathematics Magazine Vol. 54, No. 5 (Nov., 1981), pp. 227-243. jstor.org/stable/2689983?seq=1 $\endgroup$
    – Gerry Myerson
    Commented Jun 22, 2020 at 7:38
  • $\begingroup$ @GerryMyerson Thank you very much ! $\endgroup$
    – Alexander Chervov
    Commented Jun 22, 2020 at 8:02

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