Geodesic
On perfect form~$A_n^k$: existence of lattices with non-fundamental simplex of division; existence of perfect forms, which are not reducible in the sense of Minkowski to a~form with coefficients
Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 2, Tome 33 (1973), pp. 65-71

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@article{ZNSL_1973_33_a3,
     author = {S. S. Ryshkov},
     title = {On perfect form~$A_n^k$: existence of lattices with non-fundamental simplex of division; existence of perfect forms, which are not reducible in the sense of {Minkowski} to a~form with coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {65--71},
     publisher = {mathdoc},
     volume = {33},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1973_33_a3/}
}
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S. S. Ryshkov. On perfect form~$A_n^k$: existence of lattices with non-fundamental simplex of division; existence of perfect forms, which are not reducible in the sense of Minkowski to a~form with coefficients. Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 2, Tome 33 (1973), pp. 65-71. http://geodesic.mathdoc.fr/item/ZNSL_1973_33_a3/