This is because minerals with common anions share many common physical properties. Net charge on the anion group is -4. Olivine is an example. Also the most dense of the silicates due to the close packing of the tetrahedra. Due to cation-tetrahedra bonds there are no stronger or weaker bonds and hence no cleavage.
Single chains share two basal oxygen while the double chain shares three.
Involves sharing of all basal oxygens to form a sheet of silicate tetrahedra. On top of this layer is a layer of cations, then another sheet of silicates, etc. etc. This gives the well developed basal cleavage in this group. Common sheet silicates are the micas. All four oxygens are shared to build up a framework of tetrahedra.