A Choquet simplex is a closed convex and metrizable subset of a locally convex Hausdorff topological vector space in which every point is a barycenter of an unique probability measure supported on the set of extreme points. The Poulsen simplex is an unique nontrivial compact Choquet simplex with the dense set of extreme points. This was proved by Lindenstrauss, Olsen and Sternfeld [Ann. Inst. Fourier (Grenoble) 28 (1978), no. 1, vi, 91–114.] (see also http://www.ams.org/mathscinet-getitem?mr=500918). The Poulsen simplex has many remarkable properties. Is there a similar object in the category of non-necessarily compact (but bounded) Choquet simplices?