Spin is the mass/angular momentum/cover perceived on a point-particle, and hence its intrinsic observable. The immediate relation between spin and dimensions of existence follows.
As each spin number position means 1/2 dimension; so particles with 1/2,, -1/2 have 2 1/2 dimensions which create a more limited form than a boson with 3 positions or a dimensions or a graviton with 5 dimensional positions. And it follows that larger beings with more relative dimensions will have particle wise with more dimensions. So gravitons are for the larger scale, bosons for the intermediate and particles within the inner region of atoms, creating a symmetry between number of dimensions in spin terms and size of the world they exist within.
The question then as dimension can be changed and we do have a few to choose between, is which kind of dimension is the spin about?
It seems that we cannot have more than 2 half dimensions of the same species, which basically means fermions have 1/2 and 1/2 dimensions of circular, angular momentum to complete an intrinsic external membrane (±1/2) while bosons have also a degree of freedom or lineal dimension of momentum to escape its fixed positions, and that is all. Finally the graviton has even more dimensions to enclose the other particles.