How many possible H3 GeoBoundary vertex configurations are there?

Question

When getting the vertices of an H3 cell using H3toGeoBoundary, how many possible vertex configurations can the GeoBoundary struct produce? I count four:

• 6 vertices: regular hexagon
• 5 vertices: regular pentagon
• 7 vertices: irregular hexagon (https://observablehq.com/@nrabinowitz/h3-index-inspector#85080013fffffff)
• 10 vertices: irregular pentagon (https://observablehq.com/@nrabinowitz/h3-index-inspector#85080003fffffff%0A%0A)

Is this list exhaustive or can other configurations exist? Would it also ever produce 0?

Answer 1

Your list is missing the 8 vertices case. Rather than using the generic term "irregular", it's more accurate to consider extra distortion vertices: At odd resolutions, cell edges that cross an edge of the icosahedron will have additional distortion vertices added to account for the change in projection plane (at even resolutions, the cells are aligned with the icosahedron edges and do not require this). With that explanation, the list looks like this:

• 5 vertices: even-resolution pentagon cell (8408001ffffffff)
• 6 vertices: standard hexagon cell (85283473fffffff)
• 7 vertices: hexagon cell with an icosahedron edge crossing one vertex and one edge (85080013fffffff)
• 8 vertices: hexagon cell with an icosahedron edge crossing two edges (850802a3fffffff)
• 10 vertices: odd-resolution pentagon cell (85080003fffffff)

Note that we still use "pentagon" and "hexagon" to describe these cells, because that's still topologically correct (a pentagon always has 5 neighbors, a hexagon always has 6).