  In a previous article [JHEP 1111 (2011) 072; arXiv:1108.4965] we have
developed a Lorentzian version of the Quantum Regge Calculus in which the
significant differences between simplices in Lorentzian signature and Euclidean
signature are crucial. In this article we extend a central result used in the
previous article, regarding the realizability of Lorentzian triangles, to
arbitrary dimension. This technical step will be crucial for developing the
Lorentzian model in the case of most physical interest: 3+1 dimensions.
  We first state (and derive in an appendix) the realizability conditions on
the edge-lengths of a Lorentzian n-simplex in total dimension n=d+1, where d is
the number of space-like dimensions. We then show that in any dimension there
is a certain type of simplex which has all of its time-like edge lengths
completely unconstrained by any sort of triangle inequality. This result is the
d+1 dimensional analogue of the 1+1 dimensional case of the Lorentzian
triangle.
