I am in need of a way to represent the sum
$1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33$
in a geometrical way. What I mean by this is that for example, the sum
$1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30$
can be represented geometrically as a pyramid with layers consisting of 1, 4, 9 and 16 pieces respectively a regular manner. Image from Wikipedia to illustrate the geometrical construction of the square numbers.
I have tried to find such a regular pattern to construct a geometrical shape from the factorial numbers, but to no avail. How could this be done?
Also, a follow up question: Is there a way to represent the factorial numbers up to an arbitrary number $n!$, instead of ending at $4!$ as stated in this question above? (less important, but interesting nonetheless)
Thanks in advance!
EDIT: The probably most important part is that the 1, 2, 6 and 24 are discrete and somewhat separated from each other, kind of like the different layers in the comparison between te sum of squares (see linked image above).