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You can almost draw a congiguous hexagon map on a subdivided icosahedron, if you subdivide each triangle edge in 3 parts on each recursive step. Adjacent triang
by exDM69 10y ago
You can almost draw a congiguous hexagon map on a subdivided icosahedron, if you subdivide each triangle edge in 3 parts on each recursive step. Adjacent triangles will form hexagons.
This will leave 20 pentagons where the vertices of the original icosahedron's vertices were located. The rest of the sphere can be covered with a regular hexagon map for a strategy game.
I've been thinking about "hiding this" in a game design element so the 20 pentagons would be "capitals" or otherwise special tiles in the game. They're nicely equidistant from each other, so it could make a nice and fair map to play on.
- Waterluvian 10y agoThe game RimWorld does exactly this.
- amitp 10y ago(Author here) I had been trying to hide the 12 pentagons on the game map but RimWorld stretches the hexagons so that it doesn't have to hide anything. You can see one here: http://steamcommunity.com/sharedfiles/filedetails/?id=823772724 http://steamcommunity.com/sharedfiles/filedetails/?id=823772... Once you build a colony anywhere though, the colony map is square so it doesn't matter if you're on a hexagon tile or a pentagon tile.
- Waterluvian 10y agoInteresting. I thought RimWorld hid a few pentagons. Maybe the creator changed that plan?
- robinhouston 10y agoAn icosahedron has 12 vertices, so you get 12 pentagons.
- exDM69 10y agoYou're correct. 12 vertices, 20 triangles.