This is equivalent to the max-determinant problem for sign matrices, a long-well-studied problem. Regular simplices are not maxvol (but are when Hadamard matrices exist... in 3 mod 4 dimensions...) the maxvol simplex always has simplex vertices=cube vertices, as you can prove by contradiction - otherwise the matrix row that was not all +1 and -1 could be altered to make it all +1 and -1 without decreasing the |determinant|. The maxvol regular simplex, however, need not obey this property.