This gives an output, although it may not be exactly what you want:
p = {0, 0, 0};
wx = {0, 0, 1};
line = {{-1, 0, 0}, {1, 0, 0}};
b = Ball[];
Region[RegionUnion @@ Table[RegionDifference[
TransformedRegion[Cylinder[line, 1/8],
RotationTransform[i, wx, p]], b],
{i, 0, Pi, Pi/4}]]