Curved Trivalent Tree Pendant

A mathematical tree is a graph (vertices connected by edges) with no loops. A tree is regular if the number of edges attached to each vertex is the same, and that number is called the valence of the graph. Trivalent means the valence is 3. An infinite trivalent tree starts from some vertex, and has three edges coming out of it. The ends of each of those 3 edges are vertices out of which two more edges extend (to make the valence 3), giving 6 new vertices and 6 more edges. The ends of each of those 6 edges are vertices out of which two more edges extend, giving 12 new vertices and 12 more edges. That process goes on ``ad infinitum" (forever), producing the full trivalent tree. To draw part of that tree we have to make the lengths of the edges shrink as we go out from the center vertex, since otherwise they will overlap. This pendant goes out five steps, showing 48 ``ends" and a total of 93 edges. A loop for a chain has been added to the back of one of the central edges, but that should not be visible when it is worn. This is a curved version of this pendant, where the entire tree is positioned on part of a sphere, and with each edge curved, giving a more organic appearance. Thanks to Jonathan and Evelyn Clowes for suggesting these variations to the original flat linear design.