Water H2OH2O is not named as an oxide, it is in fact a treated as hydrogen hydroxide which covers it as both an acid and base. In oxides the two oxygen atoms alternate (in 3D) with other atoms, and even though this is true for ice it is still not called an oxide due to the hydroxy functionality. The oxide naming is however acceptable for deuterated and tritiated homologues, because there are no simple names. Deuterium hydroxide is fine for example, but deuterium deuteroxide is indeed simplified to deuterium oxide in common use.
H2O2H2O2 is hydrogen peroxide. Peroxy compounds contain the −O−O−−O−O− bond structure with the oxygens bridged. The meaning of "per" in chemistry is "additional", in relation to the oxygen held by a substance. So permanganate holds more oxygen than manganate for example. If the oxygen atoms are bridged anions O−2O2− then the structure is known as a superoxide (old name hyperoxide).
So that brings us to the formula HO∗2HO2∗ which is the reactive perhydroxyl or hydroperoxyl radical with bridged oxygens. It is an important species in cells and atmospheric ozone processes. Radicals have an unpaired electron, which represents an unsatisfied valence, indicated by the asterisk.
