The Euclidean pentrealm is a flat, infinitely large five-dimensional space following the rules of five-dimensional Euclidean geometry. It can be created by taking the Cartesian product of five copies of the Euclidean line. A pentrealm can be used to bisect an ecton, and polyexa can have pentrealms of symmetry through which they can be reflected. One way of viewing the structure of a polyexon is to view the realmic cross sections of the flunic cross sections of the pentrealmic cross sections of the shape.