This is how it looks in Fancade. Here we use the fact that cotangent of an angle is equal to its cosine divided by its sine:

Now, to calculate the positions of the remaining pieces, we can subtract **A** from the position of the original object and then add **A** rotated by a certain angle. Here's how it looks:

For **N** = 6 and **X** = **Z** = 1, we obtain the exact same hexagon as in the classic method, without using any additional lists! After changing the value of **N**, we can obtain different polygons, for instance a pentagon: