Dodecagonal number

A dodecagonal number is a figurate number that represents a twelve-sided polygon, known as a dodecagon. The \(n\)-th dodecagonal number can be calculated using the formula: \[ P_{12}(n) = 6n^2 - 6n + 2 \] where \(P_{12}(n)\) denotes the \(n\)-th dodecagonal number.