It is tedious. First you have to get rid of the faces [a, x>>Faces only] or you’ll wind up with a lot of unneeded edges to delete later. Add the number of new vertices you’ll need along an edge by using Multi-Subdivision [W>>Subdivision Multi, number, OK]. Change the pivot point to the 3d cursor [Hotkey= keyboard period]. Snap the 3d cursor to one point of the star [select the vertex, Shift+S>>Cursor to Selection]. Select one of the new vertices and slide it into postition using scale (it will move toward or away from the pivot point.)
Slightly easier but less accurate: Deselect the pentagram object and use it for a template. Add a new object (doesn’t matter what) and erase all the vertices [x>>vertices]. Then create a cloud of unconnected vertices [Ctrl+LMB, a to deselect, repeat several times, then a to select all and duplicate several times with Shift+D]. Select single vertices from the cloud and move them over your template, positioning them at the intersections and end points. Erase any unneeded cloud vertices. Select the vertices four at a time and create faces[f]. Straighten the edges out by box selecting a horizontal row of vertices, then scaling to zero (assuming top view, use s,y,zero). If the pentagram is pointing up, there should be two horizontal rows of vertices to straighten out. Once these are done, rotate the pentagram 72 degrees[r, 72], and a new arm will be horizontal, straighten this one out, and repeat until everything is lined up.