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We solve several new sharp inequalities relating three quantities amongst thearea, perimeter, inradius, circumradius, diameter, and minimal width of planarconvex bodies. As a consequence, we narrow the missing gaps in each of themissing planar Blaschke-Santal\'o diagrams. Furthermore, we extend some ofthose sharp inequalities into higher dimensions, by replacing either theperimeter by the mean width or the area by the volume.

Narrowing the gaps of the missing Blaschke-Santal\'o diagrams