Forty-three years ago, Geoffrey Shephard published an influential list of open problems on convex polyhedra. Progress has been made on several of his problems, and perhaps some have been completely solved. I am wondering if anyone has written a survey that updates the status of all 20 problems? Thanks for any pointers!
"Twenty Problems on Convex Polyhedra: Part I." G. C. Shephard. The Mathematical Gazette, Vol. 52, No. 380 (May, 1968), pp. 136-147. (JSTOR link). "...: Part II." No. 382 (Dec., 1968), pp. 359-367. (JSTOR link).