Hi, I am the president of the PYXIS innovation and the inventor of the indexing used on the ISEA hexagonal tessellation that you are discussing on this thread. I thought I might be able to help you out.
We call the entire mechanism a digital Earth reference model (DERM) as it encompasses the principals of a digital as opposed to an analogue way of encoding information - think of the way a sound signal (music) is encoded digitally as opposed to analog and you will mostly get the difference between the DERM and conventional coordinate systems used to reference the Earth like lat and long. Of course gamers have been well aware of the difference between such things for many years and much of the original ideas for PYXIS goes back to my own gaming days in the 70's.
So our first job was to select an optimized discretization strategy - tiling - of the Earth surface. Hexagons are generally best under most criteria however they do not aggregate and decompose congruently - like squares and triangles can - into self similiar parts. How does one create a hierarchical multi-resolution hexagonal mesh? Further studies have suggested that the ideal criteria for a Earth tilling would have each cell the same area. This is also a challenge and you have discovered that its impossible to cover the Earth with the same tile and preserve both shape and area over 20 cells - this is why there are so many patents for golf balls.
We adopted a solution called the Snyder Equal Area Icosahedral Aperture 3 Hexagonal grid (ISEA3H) first proposed by some researchers at Oregon State University who were looking at sampling for biodiversity analysis. This is a base 3 system where the grid changes by a square root three distance between cells each resolution. The area is preserved in each cell - not a meaningful trait for gaming but essential in an discrete Earth reference where statistically valid sampling of information should be preserved at any point on the planet. As noticed the exception is the 12 pentagons that will form at the vertices of the icosahedron - these are strategically placed in large water bodies for the most part - any are really really tiny for most any application - though we do have to heed them heuristically.
The indexing (addressing), mathematics (from neighbour operations to advanced algebra) and quantization strategy (sampling) are all developed and available for the grid in our library. The core value being that real time data can be synchronized to the grid and therefor multi-source analysis of Earth observations is enabled without need for a manual preprocessing typical of digital cartography and GIS. I good application for this is Geospatial-Intelligence where spatial data is brought together on the fly.
I think that if one thinks of gaming as a simulation and one uses real data to feed into that simulation, there may be some value for a game. Its rather high fidelity for a game I would expect.
If you want to look at the DERM in more detail take the following steps:
1. Down load the prototype browser on our web site - worldview -
https://www.pyxisinnovation.com/downloads.php
2. Click off the 2 default data sets
3. Activate the navigation pain by picking on it - then select the numbers 0, 2 and 4 on your key pad - this will show 4 resolutions of the ISEA3H grid - it is skipping intermediate resolutions. The entire grid is pretty dense.
4. At the bottom left there is an indicator of lat long, change this to PYXIS indexing. This will show you the index of each cell at the display resolution. Note that the display resolution is tiny - smaller than the pixels on your monitor - so you won't see them. There are 265 cells in the smallest grey cells you see on the screen.
5. Use your scroll button or +- buttons to zoom in. At resolution 40 the cells are 2 mm apart.
6. You can populate the cells with almost any conventional georeferenced imagery, vectors or terrain. Just drop the file from your windows exporer into the library on the left of the screen. Its a P2P system so you can also publish your data others.
If there is anyone interested in further information I suggest contacting us at our office 1-877-389-6619 or see website and I can have one of our engineers provide you with more.
Hope that helps out and appreciate your interest.
Regards, Perry