several of the graph's properties follow immediately from this construction. it has formula_6 vertices, because the number of points in an affine space is the size of the base field to the power of the dimension. for each affine point, there are 56 lines through cap set points, 56 triangles containing the corresponding vertex, and formula_7 neighbors of the vertex. and there can be no triangles other than the ones coming from the construction, because any other triangle would have to come from three different lines meeting in a common plane of formula_2, and the three cap set points of the three lines would all lie on the intersection of this plane with formula_1, which is a line. but this would violate the defining property of a cap set that it has no three points on a line, so no such extra triangle can exist. the remaining property of strongly regular graphs, that all non-adjacent pairs of points have the same number of shared neighbors, depends on the specific properties of the 5-dimensional cap set.