  We show that the set of $d$-variate symmetric stable tail dependence
functions, uniquely associated with exchangeable $d$-dimensional extreme-value
copulas, is a simplex and determine its extremal boundary. The subset of
elements which arises as $d$-margins of the set of $(d+k)$-variate symmetric
stable tail dependence functions is shown to be proper for arbitrary $k \geq
1$. Finally, we derive an intuitive and useful necessary condition for a
bivariate extreme-value copula to arise as bi-margin of an exchangeable
extreme-value copula of arbitrarily large dimension, and thus to be
conditionally iid.
