Closed surfaces with Euler characteristic $-2$

Euler characteristic $-2$ means orientable genus $2$ or nonorientable genus $4$.Suggest a slogan

Let $\Sigma$ be a connected closed surface with Euler characteristic $\chi(\Sigma) = -2$. If $\Sigma$ is orientable, then $\Sigma$ is homeomorphic to the orientable surface $\Sigma_2$ of genus $2$; otherwise $\Sigma$ is homeomorphic to the nonorientable surface $N_4 = \#_{i=1}^4\RP^2$ [@Mun00]; [@Hat02].

Which closed surfaces have $\chi = -2$?