In this paper, we examine the number of equivalence classes of pentagons on finite projective planes of prime order under projective transformations. We are interested in those pentagons in general position, meaning that no three vertices are collinear. We consider those planes which can be constructed from finite fields of prime order, and use algebraic techniques to characterize them by their symmetries. We are able to construct a unique representative for each pentagon class with nontrivial symmetries. We can then leverage this fact to count classes of pentagons in general. We discover that there are (1/10)((*p*+3)(*p*-3)+4*r _{p}*) such classes, where

demonstrating that any d -dimensional tile set that can tile periodically along d − 1 axes must be able to tile periodically along all axes.

This work also summarizes work on Wang Tiles up to the present day, including

definitions for various aspects of Wang Tilings such as periodicity and the validity of a tiling. Additionally, we extend the familiar 2D definitions for Wang Tiles and associated properties into arbitrary dimensional spaces. While there has been previous discussion of arbitrary dimensional Wang Tiles in other works, it has been largely informal. This work formalizes and proves several key assertions that previous work has referenced as folklore, including the fact that periodicity of a tiling is captured by a lattice. ]]>