We study the band structure of twinned and detwinned BaFe$_2$As$_2$ using angle-resolved photoemission spectroscopy (ARPES). The combination of measurements in the ordered and normal state along four high-symmetry momentum directions $Gamma$/Z--X/Y enables us to identify the complex reconstructed band structure in the ordered state in great detail. We clearly observe the nematic splitting of the $d_{xz}$ and $d_{yz}$ orbitals as well as folding due to magnetic order with a wave vector of $(pi,pi,pi)$. We are able to assign all observed bands. In particular we suggest an assignment of the electron bands different from previous reports. The high quality spectra allow us to achieve a comprehensive understanding of the band structure of BaFe$_2$As$_2$.
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