Recall that internalisation turns one square into four. This occurs in the category of (stable) trees, discussed in Leinster's book Higher Operads, Higher Categories
from page 230. For example, consider the square in the diagram.
This square is one of the three squares on the 9 faced Stasheff polytope, which one obtains by reducing the 5-leaved tree quadruple squares to ordinary faces, yielding a kind of classifying space. This diagram makes the contraction and expansion moves on trees more explicit. Recall that the entire polytope is labelled by a simple 1-level tree as befits a 1-operad polytope.
Observe that the total number of squares describing the Stasheff polytope is 6x5 (for the pentagons) plus 3x4 (for the squares) which comes to 42