The strength of the tank along the front and back are due to the vertical pieces of glass. In the vertical position, the glass has a high second area moment of inertia, which means it has a high resistance to bending. This is why I-beams are so strong and lightweight. Their strength comes from the center vertical web. Glass (especially tempered glass) is much stronger than most people think, it just has almost no ductility- it's extremely brittle. As long as the front and back panes are completely vertical (i.e. all corners perfectly level), then those panes act much like I-beams would and easily support the weight of the tank. What breaks tanks is any twisting of those panes... Because of it's low ductility, any twisting builds stresses that glass can only relieve by cracking (annealed) or shattering (tempered).
If you look at most store-bought stands, the tank doesn't touch in the centers anyways. Most people attribute this to poor manufacturing standards and throw some foam or something under the tank to "even it up." In reality, the only real concern is that all four corners are perfectly level and no torsional stresses are introduced to the glass.
Of course, the best course of action is to err on the cautious side and support the tank all the way around its perimeter. This can lead to other issues however, since then the entire stand needs to be absolutely level. Any "high spots" along the perimeter will introduce a point stress that is much more detrimental to the structural integrity than a stand that only supports the corners, as the stresses introduced in the corners-only case follow a uniform and predictable distribution and are spread throughout the entire length of the pane.
In short, a fully supported stand that is perfectly level all the way around provides the highest factor of safety. A stand with all four corners supported and completely level will provide a satisfactory factor of safety and you'll never have any issues unless the tank is of odd dimensions (in which you may need to calculate if only supporting the corners is indeed safe). The main concern should always be making sure the corners are level and no point stresses are introduced anywhere.
Last edited by Indychus; 05-02-2013 at 03:48 AM.