Update to Shephard's "Twenty Problems on Convex Polyhedra"

Question

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).

Answer 1

A listing from 1991 is given in Unsolved Problems in Geometry (Croft, Falconer, and Guy). Chapter B contains 25 open problems on polygons, polyhedra, and polytopes, including some from Shephard's 1968 list.

For updates on specific problems from Shephard's list, see

• Equiprojective polyhedra (2008).
• Moser's Shadow Problem (2013).
• (Non-)Equiprojectivity and (Non-)Biprojectivity of Simplicial Polyhedra (2010).