Gondwana broke apart along a truncated icosahedral fracture system that minimized total crack length and therefore required the least work to nucleate and propagate new fractures across the supercontinent. The fracture arrangement met conditions imposed by Euler's rule for ordering polyhedrons on a spherical shell. Linear grabens accumulated Permian rift facies along 10,000 km of the fracture system in east Gondwana. Large igneous provinces erupted >100 m.y. later along these fractures. This suggests that widening of existing fractures rather than impingement of deep-mantle plumes triggered outbreaks of flood basalt. The tensile stress field that initiated the fractures was symmetrical with...