Wow, that's a really fascinating problem to work on. I work in mapping but haven't actually come across this field of what you call DGGS's.
replyIs it essential that the cells be the same shape?
Also where does the name "A5" come from exactly? I get that 5 is because it has five sides, but why A?
The cells being the same shape is useful in some use cases and irrelevant in others. For example, see the Airbnb demo: https://a5geo.org/examples/airbnb. The H3 tiles are very different sizes in the two cities, and make it appear that there is a much higher density of listings in Malta, even though that is not the case.
replyHowever the symmetry of H3’s hexagonal cells lends itself well to flow analysis, or routing - which is no surprise as it was developed at Uber.
As for the name, it follows the convention of S2 and H3, which come from group theory and refer (loosely) to the symmetry groups of the various systems
Is it based upon repeated subdivision of an icosahedron?
replyNo, it is based on applying a lattice onto the faces of a dodecahedron (technically a pentakis dodecahedron). Take a look at https://a5geo.org/examples/teohedron-dodecahedron and other examples on the website.
replyH3 is based on a dodecahedron it is it the reason the cell areas range so much, the same is true of S2 - but this is based on a cube.