Right, so you've solved Stars #1 and know that I've based these puzzles on unique stars you can draw without lifting your pencil from the paper.
Oh, and where did I say there would be no red herrings?
Now, it's time to introduce you to Ludwig Schläfli who's going to help you solve the final puzzle in this series.
Ludwig Schläfli was born in Switzerland in 1814 and he invented the notation for polygons, polyhedra and polytopes I'm going to introduce you to.
For polygons, the Schläfli symbol has two parts: the first(n) tells you how many points - technically vertices - the shape has, while the second(p) tells you how many points around the polygon you join together.
For example, This: 
has a Schläfli symbol of 7,1; while 
is 7,2.
Finally, 
has the Schläfli symbol 7,3.
It doesn't matter from which vertex you start or which direction you go around, the notation is the same: so 7,4 is the same as 7,3; 7,5 the same as 7,2 and 7,6 is the same as 7,1. This mean that when n=7 there are 3 unique shapes, 2 of which are stars.
Time for the second puzzle: The cache is at:
51N 1
.
00W 0
.
You can check your answers for this puzzle on Geochecker.com.