Moderation of Convex Bodies

Everybody knows what an extreme point of a convex body is. Does this notion have an opposite? A most non-extreme point? Or: can we somehow say that a point is more or less extreme than another? In this paper we show a way to do this. We shall define the notion of moderation for points of a convex body. Then the points of largest moderation will be the moderate, those of smallest moderation the extreme points, as you would expect