Texture bestiary: From symmetry-breaking patterns to topological field configurations

Textures are topologically nontrivial field configurations which can exist in a field theory in which a global symmetry group G is broken to a subgroup H, if the third homotopy group ${\mathrm{\pi }}_3$ of G/H is nontrivial. We compute this group for a variety of choices of G and H, revealing what symmetry-breaking patterns can lead to texture. We also comment on the construction of texture configurations in the different models.