The Process
Generate Icosahedron
A sphere made purely of hexagons isn't quite possible, or if it is, I couldn't find any confirming documentation. Using an icosahedron will yield 12 5-sided cells across the surface of the grid, each one being at the original icosahedron's vertices (also known as a dodecahedron).All images curtesy of the wonderfully informative BUGS project.
- The base icosahedron
- Each face subdivided
- Project each new vertex out to the unit sphere
- This process can be repeated until you reach the total number of cells you wish
Generate Cells
Once you have reached your target cell count, it's time actually generate the cell mesh. The basic process runs as such:
- Foreach vertex in the subdivided icosahedron:
- Find all neighbor cells
- Foreach neighbor cell:
- Find the midpoint of neighbor cell and neighbor + 1 cell, this forms one section of the hexagon (or pentagon)
Level 1 - 42 Cells
Truncated Icosahedron
aka, soccer ball, buckyball
| Level 2 - 162 Cells | Level 3 - 642 Cells |
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