The PBE0/6-31G**quantum chemical method is used to determine the symmetry and equilibrium structural parameters of the molecules of [1.1.1.1]pagodane (C₂₀H₂₀, D _2h ), two dienes (C₂₀H₂₀, D _2h ), two diradicals (C ₂₀H₂₀, C _2ν ), and two dications (C ₂₀H ₂₀ ²⁺, D _2h and C _2ν ). The energy of a highly symmetric dication with a rectangular cycle is lower by 36 kcal/mole than that of a low symmetric dication with a trapezoidal cycle. The polarization interaction with liquid methylene chloride causes its decrease by 147 kcal/mole.