Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In five dimensional geometry, a truncated hexateron or truncated 5-simplex, is a uniform 5-polytope with 30 vertices, 75 edges, 80 triangular faces, 45 cells (15 tetrahedral, and 30 truncated tetrahedron), and 12 hypercells (6 5-cell and 6 truncated 5-cells). It is one of 19 uniform polytera generated from the regular hexateron (5-simplex), constructed by applying a truncation operation to the hexateron. In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range. For example, if the dates of birth of children in a school are examined, these would typically be subject to truncation relative to those of all children in the area given that the school accepts only children in a given age range on a specific date.