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As we well know, there is a spectacular geometrical interpretation of the Fibonacci sequence provided by the golden cut, and also a structure generated by the golden geometrical progression. Of a great theoretical interest is occurrence of the golden number in esthetics, architecture, music, anatomy and botany, etc.
The rectangle obtained as a limit of succesive addition of a Fibonacci type is known from ancient times (the golden cut) and has remarkable properties.The golden rectangle, taken as a "nucleus" in an iterative process of a Fibonacci type, generates a geometrical golden structure which might be considered a mathematical formalization of some philosophical concepts describe the part-whole relationship.
From this point of view, we can raise a problem whether there are any geometrical bodies extended in n-D Euclidian spaces which might generate fundamental properties of the 2-D golden cut and structure, and whether there are geometrical interpretation of some n-linear recurrences of a Fibonacci type.