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Rational tilings by ๐‘›-dimensional crosses

Rational tilings by ๐‘›-dimensional crosses

Consider the set of closed unit cubes whose edges are parallel to the coordinate unit vectors <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold e 1 comma ellipsis comma bold e Subscript n Baseline"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mo>,</mml:mo> <mml:mo>โ€ฆ<!-- โ€ฆ