Prompt please the formula of a pentagon cordinats, that calculate from the center to 5 corners, in three measured measurement.

In order to get the vertex coords of any regular 2D polygon you can use these formulas:

theta = 180/n

x = x0 + cos theta

y = y0 + sin theta

n - number of sides

(x0,y0) - center

for the first vertex. For the other ones use 2*theta, 3*theta, … n*theta.

To get the 3D coords you have to make the projection of the vertices for the plane you want.