Solution (source code)

= Solution

In this <C2v point group> convention, $z\sim A_1$, $x\sim B_1$, and $y\sim B_2$. Therefore all six <normal modes> have symmetry-allowed infrared fundamentals: $\boxed{6\text{ IR features}}$, absent accidental coincidences or vanishing intensities.

For <Raman spectroscopy>, examine the <polarizability tensor>: $x^2,y^2,z^2\sim A_1$, $xz\sim B_1$, and $yz\sim B_2$; $xy\sim A_2$ is also Raman-allowed but no $A_2$ vibration occurs here. All six vibrations are therefore Raman-active too, giving $\boxed{6\text{ Raman features and }6\text{ IR/Raman coincidences}}$. The centrosymmetric mutual-exclusion rule does not apply to $C_{2v}$ <formaldehyde>.