  The set of infinite-dimensional, symmetric stable tail dependence functions
associated with exchangeable max-stable sequences of random variables with unit
Fr\'echet margins is shown to be a simplex. Except for a single element, the
extremal boundary is in one-to-one correspondence with the set of distribution
functions of non-negative random variables with unit mean. Consequently, each
element is uniquely represented by a pair of a constant and a probability
measure on the space of distribution functions of non-negative random variables
with unit mean. A canonical stochastic construction for arbitrary exchangeable
max-stable sequences and a stochastic representation for the Pickands
dependence measure of finite-dimensional margins are immediate corollaries. As
by-products, a canonical analytical description and an associated canonical Le
Page series representation for non-decreasing stochastic processes that are
strongly infinitely divisible with respect to time are obtained.
