I have again a 3D geometry question. Suppose you have a 3D-polygon , determined by the cartesian coordinates of its points $(x_1, .... x_n)$, and edges $((x_1,x_2), \dots, (x_{n-1},x_n), (x_n, x_1))$. Note that the points of the 3D-polygon are not necessarily coplanar.
Suppose that you fix:
- $\forall i \in [1,n-1]$ , the distances $|x_{i+1} - x_i|$, and ${|x_1 - x_n|}$
- $\forall i \in [1,n-1]$ , the bond angles $\widehat{x_{i-1}x_ix_{i+1}}$ and $\widehat{x_{n}x_1x_{2}}$
Under this hypothesis, what is the number of valid configurations of this 3D-polygon ? Is it unique or is there an infinity of such configurations?
Thanks a lot for your help !