I'm doing a research project that involves subdividing a product of simplices. Specifically, I'm looking at theorem 2.4 from this paper:

math.sfsu.edu/federico/Articles/tropOMs.pdf

which references for proof:

www.emis.de/journals/DMJDMV/vol-09/01.pdf

Neither paper defines "regular subdivision" or references a definition, and other literature definitions are rare and not obviously equivalent. Can someone with more background in this field give a formal definition, and if that doesn't by itself give a reasonable intuition, some examples of regular vs. irregular subdivisions?

coherentsubdivisions inDiscriminants, Resultants, and Multidimensional Determinantsby I. M. Gelfand, M. Kapranov and A. Zelevinsky, which I think is the same as yourregular. – Mariano Suárez-Alvarez♦ Jul 8 '10 at 2:19Gröbner bases and convex polytopesis another very good reference. – Mariano Suárez-Alvarez♦ Jul 8 '10 at 2:23