Geodesic
A counterexample to Valette's conjecture
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 301-303

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We disprove a well-known conjecture of D. Vallete (1978), which states that every $d$-dimensional self-affine convex body is a direct product of a polytope with a convex body of lower dimension. It is shown that there are counterexamples for dimension $d=4$. Additional assumptions under which the conjecture is true are discussed. 
@article{TM_2011_275_a19,
     author = {A. Voynov},
     title = {A counterexample to {Valette's} conjecture},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {301--303},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_275_a19/}
}
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A. Voynov. A counterexample to Valette's conjecture. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 301-303. http://geodesic.mathdoc.fr/item/TM_2011_275_a19/