Conjectured face numbers of the Tutte polytopes

Let $n$ be a positive integer, let $0<q<1$ and $t>0$, and let ${{\text{\hskip.03cm\bf{T}}}}_n(q,t)$ denote the Tutte polytope defined in the source. Conjectured face numbers of the Tutte polytopes. For $0<q<1$ and $t>0$, the number of edges of ${{\text{\hskip.03cm\bf{T}}}}_n(q,t)$ is

$$3(n-1)2^{n-2}+1,$$

and the number of $2$-faces is

$$2^{n-5}\bigl(9n^2-29n+38\bigr)-1.$$

These formulas are based on computations of the $f$-vectors for $n=1,\ldots,10$ and are presented as a conjecture; no proof or resolution is supplied in the source.