the basics were
-working from the Top view to match the drawing
-making a 10 sided n-Side spline
-using the spline Pen tool to draw out the filling/crossing lines
-cutting the splines where necessary to have vertices for the next step
-added a polygon object, deleted the simple poly that gets created and used the Polygon Pen with vertex snapping on to make the flat version of the object
-use Move tool in points mode with Soft Selection on with Falloff set to Dome and Mode set to Center so it pulls the points up in a spherical shape
Spline.7 isn’t really needed it was just an experiment, the x-ray sphere is just to try and hit a spherical shape when pulling up with the Move tool.
While a spherical shape is not reasonably possible with that construction a small lift of the center of the polygon object looks ok, depends on what Sean’s clients are really after