$\RP^3$ has $\ZZ$ in degrees $0$ and $3$, $\ZZ/2$ in degree $1$, and zero otherwise.Suggest a slogan
The integral homology groups of \(\RP^3\) are \[ H_k(\RP^3;\ZZ) \cong \begin{cases} \ZZ & k = 0, 3,\\ \ZZ/2 & k = 1,\\ 0 & \text{otherwise} \end{cases} \] [@Hat02].
What is $H_* \mathbb{RP}^3$?