Object surface vanishes in sculpt mode

For one of my objects in a scene I’ve somehow gotten it into a mode where if I’m in solid view in sculpt mode whenever I click on it the entire object surface vanishes. If I’m in texture mode or have Textured Solid on it doesn’t vanish. If I’m in edit mode it doesn’t. If I have wire turned on in the Display options, the surface vanishes but the mesh is visible.

Other objects in the same scene don’t do this.

I’ve tried all the Display settings I can find, ALT H, and exiting and reentering, no change.

This is in 2.53