Betten, AntonKaraoğlu, Fatma2022-05-112022-05-1120220925-10221573-7586https://doi.org/10.1007/s10623-021-00999-whttps://hdl.handle.net/20.500.11776/7453The classification problem for cubic surfaces with 27 lines is concerned with describing a complete set of the projective equivalence classes of such surfaces. Despite a long history of work, the problem is still open. One approach is to use a coarser equivalence relation based on geometric invariants. The Eckardt point configuration is one such invariant. It can be used as a coarse-grain case distinction in the classification problem. We provide an explicit parametrization of the equations of cubic surfaces with a given Eckardt point configuration over any field. Our hope is that this will be a step towards the bigger goal of classifying all cubic surfaces with 27 lines.en10.1007/s10623-021-00999-winfo:eu-repo/semantics/closedAccessFinite geometryCubic surfaceEckardt pointClassificationNormal formArticleQ2WOS:0007392469000012-s2.0-85122390392Q1