Step 1: 3D Modeling
I started by created two intersecting ellipses and extruded them into 3D. I added some taper to the extruded ellipses (fig 2) and used mirror3d to create a symmetric shape (fig 3). I copied this shape 17 times (total of 18), and I arranged the shapes so that they are spaced 60 degrees from each other around a central point. This way you will be able to connect the straws in equilateral triangles (no straw cutting necessary). I added a sphere in the center to join all these shapes (fig 6).
I've attached my dwg and stl files below.