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This paper is a collection of thoughts and observations, being partly areview and partly a report of current research, on recent work in variousaspects of Gr\"unbaum colorings, their existence and usage. In particular, oneof the most striking significances of Gr\"unbaum's Conjecture in the2-dimensional case is its equivalence to the 4-Color Theorem. The notion ofGr\"unbaum coloring is extended from the 2-dimensional case to the case ofarbitrary finite hyper-dimensions.

Gr\"unbaum coloring and its generalization to arbitrary dimension