A uniform 5-polytope is a uniform polytope that exists in 5-dimensional Euclidean space. Using a Wythoff construction, the set of uniform 5-polytopes are enumerated below, grouped with the generation symmetry, although there are overlaps as different generators can create the same forms. Regulars and truncations The three regular 5-polytopes above create 2 families of uniform 5-polytopes. Using a naming scheme proposed by Norman Johnson, these are: {3,3,3,3} Family - There are 19 forms.