Tetragonal system
In the second or tetragonal system one axis (the c axis) is different from the other two, but all three are still at right angles with each other. This is saying scientifically that the lines of force are greater or less in one direction than in the other two, but they act at right angles to each other. The a and the b axes are equal and anything that happens to one of these two must happen to the other, but need not happen to the c axis. Thinking of the molecules that arrange themselves under this system of forces, it is clear that the simplest form will be a square prism, i.e., front to back, and from side to side the numbers of molecules will be equal, but up and down there will be a greater or lesser number. If the eight corners of this prism were cut, and these corner faces increased in size until they met, the resulting octahedron would be longer (or shorter) from top to bottom than from side to side or front to back, but the measurement from front to back would be equal to the one from side to side. In this system we may have the vertical edges of the prism beveled, and not have to bevel the horizontal ones, or we may bevel the horizontal edges and not the vertical ones. There is no dodecahedron in this system or in any other system than the isometric. The forms in this tetrahedral system are really a combination of the four sides of the square prism with such modifications as equally affect them all, with two ends which may be flat, or pyramidal, or modified pyramidal faces.