- Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas?
- Does every convex polyhedron have a combinatorially isomorphic counterpart whose edges all have rational lengths?
- Does every convex polyhedron have a combinatorially isomorphic counterpart whose vertices all have rational $x,y,z$ coordinates?

Can multiple conditions above be combined?

Update: all polyhedra in question are in $\mathbb{R}^3$.