Is checking the equivalence of two convex polytopes $p^{s}$ and $p^{t}$ NP-hard?
$p^{s}= CH\{ \cup <p^{s,a_1},...., p^{s,a_m}> \} $ // CH is convex hull computed on union of a polynomial number of polytopes $p^{s,a_i}$
$p^{t}= CH\{ \cup <p^{t,b_1},...., p^{t,b_n}> \}$ // CH is computed on union of a polynomial number of polytopes $p^{t,b_i}$
and
$p^{s,a_i}= \{(x_{i1},.....,x_{ik}) | l_{ij} \leq x_{ij} \leq u_{ij} (j=1,..., k); \sum_{j=1}^k x_{ij} =1 ; l_{ij}, u_{ij} \text{are non-negative rational numbers for} \; j=1,...,k\}$\
and
$p^{t,b_i}= \{(y_{i1},.....,y_{ir}) | l'_{ij} \leq y_{ij} \leq u'_{ij} (j=1,..., r); \sum_{j=1}^r y_{ij} =1 ; l'_{ij}, u'_{ij} \text{are non-negative rational numbers for} \; j=1,...,r\}$\