Geodesic
Generalized Sperner lemma and subdivisions into simplices of equal volume
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 245-254

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A generalization of the well-known Sperner lemma is suggested, which covers the case of arbitrary subdivisions of (convex) polyhedra into (convex) polyhedra. It is used for giving a new proof of the Thomas–Monsky–Mead theorem saying that the $n$-cube can be subdivided into $N$ simplices of equal volume if and only if $N$ is divisible by $n!$. Some new related results are announced. Bibl. 6 titles. 
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     author = {Boris M. Bekker and Nikita Yu. Netsvetaev},
     title = {Generalized {Sperner} lemma and subdivisions into simplices of equal volume},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {245--254},
     publisher = {mathdoc},
     volume = {231},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a16/}
}
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Boris M. Bekker; Nikita Yu. Netsvetaev. Generalized Sperner lemma and subdivisions into simplices of equal volume. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 245-254. http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a16/