We use a result on mixed Tate motives due to Goncharov [1] to show that the symbol of an arbitrary one-loop 2 m-gon integral in 2 m dimensions may be read off directly from its Feynman parameterization. The algorithm proceeds via recursion in m seeded by the well-known box integrals in four dimensions. As a simple application of this method we write down the symbol of a three-mass hexagon integral in six dimensions.
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