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A. H. Stroud has shown that n + 1 is the minimum possible number of nodes in an integration formula of degree three for any region in E". In this paper, in answer to the question of the attainability of this minimal number, we exhibit for each n a region that possesses a third degree formula with n + 1 nodes. This is accomplished by first deriving an in + 2)-point formula of degree three for an arbitrary region that is invariant under the group of affine transformations that leave an «-simplexdoi:10.2307/2004619 fatcat:dps6aadnunfufbxzxxqdsyahqa