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The Gissinger model is a low-dimensional Lorenz-like system derived from symmetry considerations to investigate dynamics in magnetic field reversals produced by the flow of an electrically conducting fluid in a spherical domain. We examines characteristics of shrimp-shaped domains, where there corresponds to periodic attractors, immersed in the chaotic regions in the two-dimensional parameter plane constructed from the largest Lyapunov exponent spectrum. Additionally, we explore the coexistence of symmetric attractors due to the Gissinger model's invariance under rotations around the z-axis.