This paper proposes new symmetries (the body-centred cubic periodic symmetries) beyond the standard model. Using a free particle expanded Schrodinger equation with the body-centred cubic periodic symmetry condition, the paper deduces a full baryon spectrum (including mass M, I, S, C, B, Q, J and P) of all 116 observed baryons. All quantum numbers of all deduced baryons are completely consistent with the corresponding experimental results. The deduced masses of all 116 baryons agree with (more than average 98 percent) the experimental baryon masses using only four constant parameters. The body-centred cubic periodic symmetries with a periodic constant ``a about $10^{-23}$m play a crucial rule. The results strongly suggest that the new symmetries really exist. This paper predicts some kind of ``Zeeman effect of baryons, for example: one experimental baryon N(1720)${3/2}^{+}$ with $ Gamma$ = 200 Mev is composed of two N baryons [(N(1659)${3/2}^{+}$ + N(1839)${3/2}^{+}$] = $bar{N(1749)}$${3/2}^{+}$ with $Gamma$ = 1839-1659 = 180 Mev.
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