Abstract. Sperner's lemma is a statement about labeled triangulations of a simplex. McLennan and Tourky (2007) provided a novel proof of Sperner's Lemma by examining volumes of simplices in a triangulation under time-linear simplex-linear deformation. We adapt a similar argument to prove Tucker's Lemma on a triangulated cross-polytope P . The McLennan-Tourky technique does not directly apply because this deformation may distort the volume of P . We remedy this by inscribing P in its dual polytope, triangulating it, and considering how the volumes of deformed simplices behave.

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