The crystallographic space groups and Heterotic string theory

While the 17 planar crystallographic groups were shown to correspond to 17 two and three Stein spaces with a total dimension equal to Dim E12 ¼ 5 ao ffi 685, the present work reveals that the corresponding 219 three dimensional groups leads to a total dimensionality equal to No ffi 8872 which happens to be the exact total number of massless states of the transfinite version of Heterotic super string spectrum.