Isometric system
When the axes are all equal and at right angles to each other, a crystal is said to be in the isometric system. The cube is the basal form and each side is known as a face. The ends of the axes come to the middle of the cube faces. The essential feature of this system is that whatever happens to one axis must happen to all, which is another way of saying that all the axes are equal. If we think of the cube as having the corners cut off, we would have a new face on each of the eight corners, in addition to the six cube faces. Then if each of these new faces were enlarged until they met and obliterated the cube faces, an eight-sided figure, the octahedron, would result. In this the axes would ran to the corners. Another modification of the cube would be to bevel each of its twelve edges, making twelve new faces in addition to the six cube faces. If we think of these new faces being developed until they meet and obliterate the cube faces, there will result a twelve-sided figure, the dodecahedron. And the 24 edges of the dodecahedron could be beveled to make a 24-sided figure, and so on. Of course in Nature the corners are not cut, nor the edges beveled, but as a result of the interaction of the forces expressed by the axes and the distribution of the molecules, the molecules arrange themselves in a cube, octahedron, dodecahedron or combination of these basal forms.