The fact that the chromatic number of the plane must be at least four follows from the existence of a seven-vertex unit distance graph with chromatic number four, named the Moser spindle after its discovery in 1961 by the brothers William and Leo Moser. This graph consists of two unit equilateral triangles joined at a common vertex, "x". Each of these triangles is joined along another edge to another equilateral triangle; the vertices "y" and "z" of these joined triangles are at unit distance from each other. If the plane could be three-colored, the coloring within the triangles would force "y" and "z" to both have the same color as "x", but then, since "y" and "z" are at unit distance from each other, we would not have a proper coloring of the unit distance graph of the plane. Therefore, at least four colors are needed to color this graph and the plane containing it. An alternative lower bound in the form of a ten-vertex four-chromatic unit distance graph, the Golomb graph, was discovered at around the same time by Solomon W. Golomb.