Octahedral complexes are polygonal complexes with octahedral graphs as links. In this paper we classify them with the aid of computer software.
More specifically, (2n,d)-octahedral complexes are 2-dimensional simply connected complexes admitting a flag transitive group of symmetries, such that each face is a d-gon, and such that each vertex link is the octahedral graph with 2n vertices.
For each d greater than or equal to 6, and each n we classify the (2n,d)-octahedral complexes in terms of properties of the group of symmetries of the octahedral graph.
With this result and some computer programs we give explicit descriptions of all (2n,d)-octahedral complexes for d greater than or equal to 6 and n less than or equal to 6.
We have partial results for d < 6. We classify (2n,3) complexes that are simplicial for all n. We give a conjectural description of all (2n,3) complexes in which simplices inject, and we give an example of a 1-vertex (14,3)-complex. We have some partial results concerning (2n,4)-complexes and we give some examples of (2n,5)-complexes.