  We study various geometrical quantities for Calabi-Yau varieties realized as
cones over Gorenstein Fano varieties, obtained as toric varieties from
reflexive polytopes in various dimensions. Focus is made on reflexive polytopes
up to dimension 4 and the minimized volumes of the Sasaki-Einstein base of the
corresponding Calabi-Yau cone are calculated. By doing so, we conjecture new
bounds for the Sasaki-Einstein volume with respect to various topological
quantities of the corresponding toric varieties. We give interpretations about
these volume bounds in the context of associated field theories via the AdS/CFT
correspondence.
