Further studies of a single crystal of alacranite with dimensions (30 × 60 × 120 mm was examined using direct methods, Fourier syntheses and structure refinement resulting in intensities violating the C lattice type and symmetries like h0l reflections with l = 2n + 1 were absent.
Lochlainn O'Raifeartaigh made contributions in the application of symmetries in theoretical particle physics and John T. Lewis had interests including Bose-Einstein condensation and Large deviations theory.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26)
Variation of the first term of the action with respect to the tetrad gives the (mixed index) Einstein tensor and variation of the second term with respect to the tetrad gives a quantity that vanishes by symmetries of the Riemann tensor (specifically the first Bianchi identity), together these imply Einstein's vacuum field equations hold.
The system becomes more chaotic as dynamical symmetries are broken by increasing the quantum defect; consequently, the distribution evolves from nearly a Poisson distribution (a) to a Wigner distribution (h).
Numerous geometric patterns and symmetries can be observed in a Vedic square some of which can be found in traditional Islamic art.