\begin{definition}[Definition:Pentatope Number]
'''Pentatope numbers''' are those denumerating a collection of objects which can be arranged in $4$ dimensions in the form of a regular pentatope.
The $n$th '''pentatope number''' $P_n$ is defined as:
:$\ds P_n = \sum_{k \mathop = 1}^n T_k$
where $T_k$ is the $k$th tetrahedral number.
\end{definition}