Let (G,u) be an unperforated partially ordered abelian group with an order unit, u. It is simple if every nonzero positive element is an order unit. By [G, ], it is archimedean if and only if for g in G, τ(g) ≥ 0 for all pure traces τ implies g ∈ G. Among unperforated groups, archimedean and simple represent properties that are maximal and minimal, respectively—the former are those for which the weakest necessary condition (that the values at traces be nonnegative) implies positivity, while the latter are those for which the strongest sufficient condition (that positivity implies strict positivity on traces) is implied by positivity. So it is a little difficult to construct dimension groups that are both simple and archimedean, aside from subgroups of the reals. Question 4 of [G] asks whether every Choquet simplex can be the trace space a of a simple archimedean dimension group; we show this is the case for metrizable simplices, based on an interesting construction over the interval. The normalized trace space of (G,u) is denoted S(G,u); the latter’s extremal boundary is denoted ∂eS(G,u). We use ˆ to denote the natural map G → AffS(G,u), given by ĝ(τ) = τ(g). An alternative formulation of simple and archimedean (in the presence of an order unit) is the following. Suppose G admits an unperforated partial ordering such that the map G → AffS(G,u) is an embedding; then the ordering is unique (the smallest ordering is strict ordering, the largest ordering is the pointwise one). The following is practically tautological.