The geometric shape of the silicate molecule - the Tetrahedron - is best envisioned as a force field rather than a solid object. In the drawing, we've done a freeze frame on forces which are in constant motion in reality.
The silicate molecule sits at the center of a tetrahedron at whose four corners are four oxygen atoms whose negative charges cause them to push as far a part from each other as possible, thus creating the tetrahedral shape.
The tetrahedron shape is widespread in the submicroscopic structure of not only minerals, but of living cells in humans, animals and plants. The shape comprised of 4 triangles is the most flexible and strongest 3-dimensional shape there is. It encompasses the smallest volume and has the largest surface area of any 3-dimensional shape. It is the only 3-dimensional shape whose every corner is exactly the same distance from every other corner.
There are five other crystal systems besides the tetragonal. These are explored on the Crystallography page that follows.