Simple model renders strange in JME. False "faces"?

I have this simple model of a star which renders fine in blender, but in JME it does something weird.

This is just a snapshot but rotating it around shows different “faces” that shouldn’t be there, and also does so when rendering in-game.

Model files for download: model files (blend and j3o)

Why does this happen? How to fix it?

I made the model from a cube by subdividing some pairs of edges to make a new edge in between, then moved each “middle edge” towards the center of the cube a bit.