The original publication is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10127966&fileId=S0025579315000248
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[en] We investigate the decomposition problem of balls into finitely many
congruent pieces in dimension d = 2k. In addition, we prove that the
d dimensional unit ball B_d can be divided into finitely many congruent
pieces if d = 4 or d ≥ 6. We show that the minimal number of required
pieces is less than 20d if d ≥ 10.