  This paper serves to define an extension, which we call dimensional Veblen,
of Oswald Veblen's system of ordinal functions below the large Veblen ordinal.
This is facilitated by iterating derivatives of ordinal functions along
multidimensional array structures, and can be viewed as the "maximal" natural
extension of the Veblen functions. We then construct an ordinal notation based
on it, and provide a conversion algorithm from Buchholz's function below the
Bachmann-Howard ordinal.
