  We discuss properties of the $\epsilon$-expansion in $d=4-\epsilon$
dimensions. Using Lagrange inversion we write down an exact expression for the
value of the Wilson-Fisher fixed point coupling order by order in $\epsilon$ in
terms of the beta function coefficients. The $\epsilon$-expansion is
combinatoric in the sense that the Wilson-Fisher fixed point coupling at each
order depends on the beta function coefficients via Bell polynomials. Using
certain properties of Lagrange inversion we then argue that the
$\epsilon$-expansion of the Wilson-Fisher fixed point coupling equally well can
be viewed as a geometric expansion which is controlled by the facial structure
of associahedra. We then write down an exact expression for the value of
anomalous dimensions at the Wilson-Fisher fixed point order by order in
$\epsilon$ in terms of the coefficients of the beta function and anomalous
dimensions.
  We finally use our general results to compute the values for the
Wilson-fisher fixed point coupling and critical exponents for the scalar $O(1)$
symmetric model to $O(\epsilon^7)$.
