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The paper presents the construction of a rolling robot able to move in the horizontal plane due to an original structure of a regular dodecahedron shape with twelve extending legs disposed in a radial manner in the centers of its faces. A mathematical model is developed and the robot functioning is simulated. Simulation results were validated by preliminary testing. A control algorithm developed by the authors takes advantage of the symmetric shape of the robot and allows recovering from perturbations, thus increasing the resilience of the robotic system.