With[{n = 7, pent = CirclePoints[5]}, 
     Graphics[Point[Flatten[With[{div = Subdivide[Fibonacci[n]]},
                                 Transpose[{1 - div, div}].#] & /@
                            Partition[pent[[{1, 3, 5, 2, 4, 1}]], 2, 1], 1]]]]