  Non-integer dimensions are commonplace in quantum field theories (QFTs)
through dimensional regularization. In particular this affects angular
calculations involving dot products. The structure of these rises from the
generally accepted axiom that Gaussian integrals can be written as a
$d$-dimensional product of a single dimensional Gaussian integral. This result
can be extended in a straightforward manner to involve any above
zero-dimensional "surfaces", but there is somewhat clear ambiguity with
convergence when considering negative values of dimensions. This obstacle can
be answered with proper regularization strategy, which leads to an acceptable
analytic continuation. Furthermore, we suggest a method of symmetrizing the
angular calculations back to positive dimensional variants by applying the
symmetries of Euler gamma functions. Through this method, the region $d \in
[0,1]$ is recognized to be fundamentally different from either remaining
half-axis of dimensionality. By setting this region as the proper limit for the
angle generating dimension, we fully establish the rules of iterative use of
the generating method and the maximal number integration angles.
