In the 4-dimension Euclid space, $A=\{conv(P\cup Q)|P, Q \text{ are zonotopes}\}$, (all points and segments are zonotopes as well, thus all points, segment, trianges and tetrahedrons are in $A$).

Let $B=\{\text{any finite Minkowski sum of elements in $A$}\}$.

The question is that, for a 4-dimension simplex $a$, are there $b,c$ in $B$ such that $b = a+c$ (here $+$ is the Minkowski sum). By affine transformation, we can just consider the case where $a$ is $(0,0,0,0),(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)$.

Here is my attempt: I try to consider the 3-dimension version: $A=\{conv(P\cup Q)|P \text{ is a zonotope}, Q\text{ is a single point}\}$ and the define $B$ similarly. The question becomes: for a 3-dimension simplex $a$, are there $b,c$ in $B$ such that $b=a+c$.