We derive the rotation-vibration spectrum of a 3α+1 neutron(proton) configuration with triangular D_{3h} symmetry by exploiting the properties of the double group D_{3h}^{'} and show evidence for this symmetry to occur in the rotation-vibration spectra of ^{13}C. Our results, based on purely symmetry considerations, provide benchmarks for microscopic calculations of the cluster structure of light nuclei.