Triangular, pentagonal, and hexagonal

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

\[ \begin{align*} &\text{Triangle }&&Tn=\frac{n(n+1)}{2} &&1, 3, 6, 10, 15, ...\\ &\text{Pentagonal }&&Pn=\frac{n(3n−1)}{2} && 1, 5, 12, 22, 35, ...\\ &\text{Hexagonal }&&Hn=n(2n−1) &&1, 6, 15, 28, 45, ...\\ \end{align*} \] It can be verified that \( T_{285} = P_{165} = H_{143} = 40755 \).

Find the next triangle number that is also pentagonal and hexagonal.