Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far a given convex body is from one with "enough symmetries". To define these new measures of symmetry, we use affine covariant points. We give examples of convex bodies whose affine covariant points are "far apart". In particular, we give an example of a convex body whose centroid and Santaló point are "far apart".
Bibliographical noteFunding Information:
✩ Partially supported by an NSF grant, an FRG-NSF grant and a BSF grant. * Corresponding author at: Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA. E-mail addresses: firstname.lastname@example.org (M. Meyer), email@example.com (C. Schütt), firstname.lastname@example.org (E.M. Werner).
- Convex bodies
- Measures of symmetry
- Santaló point