More Characterizations of Certain Special Families of Simplices

This paper is about various characterizations of orthocentric, and other special types of, d-dimensional simplices and related issues. It puts together several three-dimensional results that are scattered in the literature, and establishes stronger versions and extensions to higher dimensions. These compactly organized results, which are mostly new for higher dimensions, are expected to be very useful tools for further research. Several open problems are posed.