We study the topological properties of compacta on which exist vector (with values in space $R^s$) systems of Chebyshev functions or systems having a given Chebyshev rank. The lengths of the systems are assumed to be multiples of but not equal to the number $s$. A compactum on which a Chebyshev system exists is embedded into space $R^s$. On polytopes of dimension $s+1$ the Chebyshev ranks of vector systems grow to infinity together with their length.