Computing symmetries of implicit algebraic surfaces.

We present a complete algorithm to compute the rotational, axial, reflectional and central symmetries of an algebraic surface defined by means of its implicit equation. The algorithms rely on the fact that the symmetries of the surface satisfy an algebraic condition verified by the polynomial defining the surface, and use a variety of ideas, some of them extensions to space of ideas already used to compute the symmetries of planar implicit curves, and some of them new. We flesh out our algorithms with several examples.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).