That will be easier done than said. 😉 Following assumes Max2014.
1. Create a 5-sided n-gon shape of a suitable size. Move it to the Origin.
2. Convert it to Editable Spline, select all the Segments, Divide (value 1).
3. Clone the object (as a Copy). Turn on Snaps (to Vertex). Hierarchy Panel, Affect Pivot Only and snap the Pivot to the vertex in the middle of the only edge which lies along the Y axis. Turn of Affect Pivot Only.
4. Rotate Tool, Use Pivot Point (transform centre) and rotate it 180 degrees so you have a mirror image of the original, touching along one edge.
5. Utilities > Reset X-Form.
6. Rotate the Clone back towards the vertical 63 degrees. NB. 63 Degrees is NOT exact, but it's mighty close and should be sufficient for a model like that. If you want perfect accuracy you'll have to investigate Geodesic Domes (BuckyBalls) to find out how to calculate the correct angle.
7. Change the Transform Centre to Use Transform Coordinate Centre (instead of Pivot Point).
Repeat the following 2 steps (8 and 9) 4 times, but omit the clone step on the last one.
8. Clone the Clone object. Select the Original object and Attach one of the clones to it (doesn't matter which).
9. Rotate the original object 72 degrees around Z.
10. You should now have something very close to the lower half of the intended result. At this point the vertices in the middles of the edges are no longer required - select and delete them.
11. Apply a Mirror Modifier and Mirror the object in Z. Apply an Edit Spline Modifier, Spline SubObject level (should already have all the splines in the mirrored copy selected). Detach as a new Shape object.
12. Rotate the new object 36 degrees (around Z).
13. Snap the mirrored object into position by grabbing one of its vertices (at a point) and use 3D Snap to Vertex to position it correctly above the original. Select the original and attach the mirror to it. Convert the object to Editable Poly.
14. You may find that one half has its polys flipped (normals facing inwards). If so simply select them and click Flip.
15. Select all the vertices and Weld them (you may need to increase the Tolerance slightly). Select all the Polys and clear the Smoothing Groups.
What you do with it then is up to you - an easy way to get something roughly like your image would be to clone the object - don't move it! Apply a semi-transparent material to one copy, apply a Lattice Modifier to the other.
