  We examine the dimensions of various inf-sup stable mixed finite element
spaces on tetrahedral meshes in 3D with exact divergence constraints. More
precisely, we compare the standard Scott-Vogelius elements of higher polynomial
degree and low order methods on split meshes, the Alfeld and the Worsey-Farin
split. The main tool is a counting strategy to express the degrees of freedom
for given polynomial degree and given split in terms of few mesh quantities,
for which bounds and asymptotic behavior under mesh refinement is investigated.
Furthermore, this is used to obtain insights on potential precursor spaces in
full de Rham complexes for finite element methods on the Worsey-Farin split.
