Abstract
We present a counterexample to the conjecture of Bihan, Franz, McCrory, and van Hamel concerning the maximality of toric varieties. There exists a six dimensional projective toric variety $X$ with the sum of the $\mathbb {Z}_2$ Betti numbers of $X(\mathbb {R})$ strictly less than the sum of the $\mathbb {Z}_2$ Betti numbers of $X(\mathbb {C})$.
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