Euler’s Gem: The Polyhedron Formula and the Birth of Topology

November’s Book of the Month is Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David Richeson, published in 2008 by Princeton University Press.
(Adapted from the Amazon description)
Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the formula’s far-reaching impact on topology, the study of shapes. David Richeson tells how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope for use with higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula.