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 Gondwana and exploited preexisting lithospheric suture zones. The stress field was also symmetrical about the African geoid bulge in the Permian locus of Gondwana. Tensile hoop stress along the Gondwana boundary initiated radial fractures that defined the lateral edges of Australia, India, Arabia, Libya, and northwest Africa. Fractures then evidently propagated inward across Gondwana, spontaneously bending at critical lengths congruent with the tessellation. Fractures later branched outward from the bends to create triple-rift junctions. Plate tectonic processes later exploited the icosahedral fractures to separate the Gondwana daughter continents.