If a GQ S′ of order (s, s) is contained in a GQ S of order (s, s2) as a subquadrangle, then for each point X of S\S′ the set of points \documentclass[12pt]{minimal}
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$$O_x $$
\end{document} of S′ collinear with X form an ovoid of S′. Thas and Payne proved that if S′= \documentclass[12pt]{minimal}
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$$Q$$
\end{document}(4,q),q even, and \documentclass[12pt]{minimal}
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$$O_x $$
\end{document} is an elliptic quadric for each X∈S\S′,thenS≅ \documentclass[12pt]{minimal}
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$$Q$$
\end{document}(5,q). In this paper we provide a single proof for the q odd and q even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex.
