Structure Prediction: Structure searches were performed using a particle swarm optimization (PSO) algorithm implemented in the Crystal structure Analysis by Particle Swarm Optimization (CALYPSO) software. Our search considered K:CO stoichiometries 2:1, 1:1, 1:2, 1:3 1:4, 2:3, 5:6, 5:12 and 7:12. For most stoichiometries, we performed a scan over the number of formula units per unit cell, ranging from 1 to 6. The exceptions are the larger 5:6, 5:12 and 7:12 ratios, where only one formula unit was considered. For each structure prediction, 30 generations of 30 structures were generated. 60 % of these structures were generated by PSO, while 40% were created by random placement of atoms. In total, we have structurally optimized approximately 35000 unit cells. Electronic Structure Theory: Structural relaxations were performed using periodic DFT implemented in VASP version 6.1.0. For structure prediction we relied on the Predew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange correlation functional 99 combined with a D3(BJ) dispersion correction. 100, 101 Numerical integrations were made over Gamma-centered k-meshes with a reciprocal space resolution < 2π•0.016 Å -1 . Our calculations relied on hard projector-augmented wave (PAW) pseudopotentials, 102, 103 that include the following valence electrons : K (3s 2 3p 6 4s 1 ), C (2s 2 2p 2 ), O (2s 2 2s 4 ). The plane wave basis set expansion was limited to 900 eV. Convergence criteria for electronic energies and forces were 10 -8 eV and 1 meV/Å, respectively. The structure of K3C6O6 was additional investigated using the Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functional, 104, 105 combined with the D3(BJ) dispersion correction, in which case we relied on standard PAW potentials for C and O.