There are actually around 20 known crystalline phases of ice, and only two of them – hexagonal ice and cubic ice – occur naturally on Earth.
Hexagonal ice, also known as Ice Ih (ice one h), is the structure of pretty much all the frozen water humans ever come into contact with on Earth's surface, while cubic ice (Ice Ic, or ice one c) is thought to sometimes form in our planet's upper atmosphere.
This article looks at creating Ice VII (ice 7), ice created under high pressure and might be found on Europa
For The First Time, Scientists Have Captured 'Alien Ice' Crystallising on Earth