  The aim of this note is to provide several variants of the diameter two
properties for Banach spaces. We study such properties looking for the
abundance of diametral points, which holds in the setting of Banach spaces with
the Daugavet property, for example, and we intro- duce the diametral diameter
two properties in Banach spaces, showing for these new properties stability
results, inheritance to subspaces and characterizations in terms of finite rank
projections.
