The first four stellations are represented below. How many dots are in the 20th stellation?

Hint: Try to figure out a pattern with the tessellations!

\(\text{stellation $n$ has an $n \times n$ square of dots, and 4 identical triangular regions containing}\\ \dfrac{n(n-1)}{2} \text{ dots each}\\ dots_n = n^2 + 4\dfrac{n(n-1)}{2} = 3n^2 - 2n\\ \text{I leave you to plug 20 in}\)

400+4*190=1160

4(1+2+3+....19)=4*190=760. Add the 19*19 square, so 760+361=1121 dots in the twentieth stellations.