Here are a few views of its medial axis, rendered as trimmed Bezier patches. Most of the sheets are planar, but four are sections of elliptical cones.
Here are a couple of views of the seams, including the edges of the original polyhedron. Most of the seams are line segments, but three are sections of ellipses. (One of the elliptical segments is too small to see here.)
A summary of the structure of the medial axis:
|Sheets||15: 11 planar, 4 conical|
|Seams||12: 9 linear, 3 ellipsoid segments|