  In this article, a new method for characterizing nontransitive dice is de-
scribed. This new method is then used to describe the "Nontransitive
Identities" (NI) that are possible for 3 dice with 3, 4 and 5 sides each as
well as for 5 dice with 3 sides each. Next, we will discuss how these NI can be
used to create NI that involve more dice and/or die sides. From there, the 3
dice Nontransitive Identities (NI) will be used to produce 5 dice NI. We will
begin this by describing more nomenclature that becomes necessary for
characterizing sets of NI with multiple win chains. Then, we will describe a
method for creating 5 dice NI and 7 dice NI from our 3 dice NI. We will
conclude with a discussion on the patterns that exist in the frequency of
nontransitive identities and how these patterns correlate to NI morphisms. Our
ancillary files will include our python scripts as well as all of the sets of
Nontransitive identities we have discussed.
