This paper extends the findings of the prior research concerning n-balls, regular n-simplices, and n-orthoplices in real dimensions using recurrence relations that removed the indefiniteness present in known formulas. The main result of this paper is the proof that these recurrence relations are continuous for complex n, whereas in the indefinite points their values are given in the sense of a limit of a function. It is shown that the volume of an n-simplex is a bivalued function for n < 0, and thus the surfaces of n-simplices and n-orthoplices are also bivalued functions for n < 1. Applications of these formulas to these omnidimensional polytopes inscribed in and circumscribed about n-balls reveal previously unknown properties of these geometric objects in negative, real dimensions. In particular for 0 < n < 1 the volumes of the omnidimensional polytopes are larger than volumes of circumscribing n-balls, while their volumes and surfaces are smaller than volumes of inscribed n-balls.