The paper describes a newly proposed combination of the two existing Duval Pentagons method utilized for the identification of mineral oil-insulated transformers. The aim of the combination is to facilitate automatic fault identification through computer programs, and at the same time, apply the full capability of both original Pentagons, now reduced to a single geometry. The thorough classification of a given fault (say, of the electrical or thermal kind), employing individual Pentagons 1 and 2, as originally defined, involves a complex geometrical problem that requires the build-up of a convoluted geometry (a regular Pentagon whose axes represent each of five possible combustible gases) to be constructed using computer language code and programming, followed by the logical localization of the geometrical centroid of an irregular pentagon, formed by the partial contribution of individual combustibles, inside two similar structures (Pentagons 1 and 2) that, nonetheless, have different classification zones and boundaries, as more thoroughly explained and exemplified in the main body of this article. The proposed combined approach results in a lower number of total fault zones (10 in the combined Pentagons against 14 when considering Pentagons 1 and 2 separately, although zones PD, S, D1 and D2 are common to both Pentagons 1 and 2), and therefore eliminates the need to solve for two separate Pentagons.