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We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} forthe cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in[n]. First, we find an extended formulation of size log(n) for d= 2. Then, weuse this as base case to construct small-rank nonnegative factorizations of theslack matrices of higher-dimensional cyclic polytopes, by iterated tensorproducts. Through Yannakakis's factorization theorem, these factorizationsyield small-size extended formulations for cyclic polytopes of dimension d>2.

Small Extended Formulations for Cyclic Polytopes