Mathematics and physics extend the notion of dimensionality beyond the usual perception of three dimensions to consider higher-dimensional spaces. The formulae describing properties such as area and volume of some geometric objects can result in indefiniteness, particularly when dealing with negative dimensions.

Dr Szymon Łukaszyk, an independent researcher in Poland, has discovered recurrence relations that can remove the indefiniteness in these formulae. His investigation into the properties of regular convex polytopes and balls reveals previously unknown properties of these objects in negative dimensions.

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Read some of their latest work here: https://doi.org/10.3390/math10132212