Finding the endpoint of a vertex given startpoint of vertex and midpoint of shape

Question

Given that:

• The shape is a regular polygon in 3D space
• The start point (the end of one arbitrary vertex of the shape) is known
• the point in the middle of the shape (not on an edge - equidistant from all corners) is known

the angle at each corner (((numEdges-2)*PI)/numEdges), the radius of the shape (distance from a corner to the midpoint = sqrt(dx^2 + dy^2 + dz^2)), and the length of each edge (radius*2*sin(pi/numEdges)) can be calculated.

Given all this information, is it possible to fill in the blanks, if you like, and work out the rest of the start/endpoints for each vertex of the shape?

I can sort of see the beginnings of the logic in 2D, but in 3D i'm lost.

Answer 1

I'm thinking it can't be done, since your knowns do not uniquely identify your polygon. The points you do know define a unique line, but I can provide infinitely many congruent polygons with the same vertex and center, all rotations of one another about this line.