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Background: Recently, Bijker et al. [Phys. Rev. Lett. 122, 162501 (2019)] explained the rotation-vibration spectrum of 13 C by assuming a triangular nuclear shape with D 3h symmetry. Purpose: The purpose of this work is to test the shape and symmetry of 13 C based on a microscopic nuclear model without assumption of nuclear shape. Method: We have applied the real-time evolution method to 13 C. By using the equation-of-motion of clusters, the model describes the 3α + n system without any assumption of symmetry. Results: REM described the low-lying states more accurately than the previous cluster model studies. The analysis of the wave functions showed that the ground band has approximate triangular symmetry, while the excited bands deviate from it. Conclusion: This work confirmed that the ground band has the intrinsic structure with the triangular arrangement of three α particles.

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