A unified recursive method is proposed for constructing magic hypercubes in d-dimensional space for any order n ≥ nbase, where nbase = 3 for d = 2 and nbase = 5for d ≥ 3. The elements form an arbitrary arithmetic progression with first terma ∈ R and common difference g ∈ R \ 0. The key feature of the method is complete fractal nesting: every sub-hypercubealigned with the recursive division grid at any hierarchy level is itself a magic con-struction. The method is universal, mathematically rigorous, conceptually transpar-ent, and computationally efficient even for very large orders n and high dimensions. When appropriate base templates are used, it is possible to obtain fully perfect (nasik) constructions at all hierarchy levels. Русская версия статьи доступна в дополнительном файле.
Khusein Ismailovich Khamchiev (Tue,) studied this question.