If you aren’t familiar with Pascal’s triangle, it’s a way of arranging numbers in rows. The first row only has a single number: 1. The second row has two numbers: 1 and 1. From then onwards, each row ...

Rows zero through five of Pascal’s triangle. The pattern continues on into infinity. Two of the sides are filled with 1's and all the other numbers are generated by adding the two numbers above.

So the first row is just 1; the second row is 1, 1; the third row is 1, 2, 1; the fourth row is 1, 3, 3, 1; then 1, 4, 6, 4, 1; and so on. We keep calling this pattern “Pascal’s triangle ...

So the number of vertices these slices have are 1, 3, 3, 1, which corresponds to the third row in Pascal's triangle. The first diagonal slice intersects one vertex-- 0, 0, 0.