(TFT) Mark's equal-area-icosahedral map

[Rick Smith <rsmith@lightspeed.ca>]

Hi Mark, everyone.
  The map below is called an equal-area-icosahedral 
projection.  Note that 12 of the hexagons are really
pentagons but both (hexes and pentagons) represent
the same area.

  GURPS Space uses this for its maps of worlds and 
I quite like it.

  It does work at the north and south poles but they
are cut into 5 wedge shapes, so usually GURPS Space
gives an area about 3 hexes in radius showing the 
poles (with a wedge cut into it).  Usually they put
boring terrain at both north and south poles so it
does not matter as much.

  Note that you can greatly increase the number of
hexes, but you always have 12 pentagons.

  Warm regards, Rick.


On Sun, 2008-16-03 at 20:46 -0500, Mark Tapley wrote:
> 	Sure hope you are reading this next in a non-proportional font....
> 
> 	Turn the below map on its side. Each triangle, marked at its 
> corners, will remain flat. There are 5 triangles to the left 
> ("North"; triangles 1-5) and 5 to the right ("South"; triangles 
> 16-20). Cut out and fold slightly back on triangle boundaries. North 
> pole is where all the (originally) left-most triangles meet when they 
> are folded together and south pole is where all the right-most 
> triangles meet when they are folded together. There are some 
> funny-sided "hexagons" to deal with at triangle corners, but that's a 
> detail :-) Triangles 6 and 15 meet along their free edges to complete 
> the "equatorial" band of triangles.
> 
> 
>                  __
>               __/ 6\__
>            __/ 1\__/  \__
>         __/  \__/  \__/  \__
>      __/  \__/  \__/  \__/ 6\__
>     / 1\__/  \__/  \__/  \__/ 7\__
>     \__/  \__/  \__/  \__/  \__/16\__
>        \__/  \__/ 6\__/  \__/  \__/  \__
>           \__/ 1\__/ 7\__/  \__/  \__/  \__
>              \__/ 8\__/  \__/  \__/  \__/16\
>            __/ 2\__/  \__/  \__/  \__/  \__/
>         __/  \__/  \__/  \__/ 7\__/  \__/
>      __/  \__/  \__/  \__/ 8\__/16\__/
>     / 2\__/  \__/  \__/  \__/ 9\__/
>     \__/  \__/  \__/  \__/  \__/17\__
>        \__/  \__/ 8\__/  \__/  \__/  \__
>           \__/ 2\__/ 9\__/  \__/  \__/  \__
>              \__/10\__/  \__/  \__/  \__/17\
>            __/ 3\__/  \__/  \__/  \__/  \__/
>         __/  \__/  \__/  \__/ 9\__/  \__/
>      __/  \__/  \__/  \__/10\__/17\__/
>     / 3\__/  \__/  \__/  \__/11\__/
>     \__/  \__/  \__/  \__/  \__/18\__
>        \__/  \__/10\__/  \__/  \__/  \__
>           \__/ 3\__/11\__/  \__/  \__/  \__
>              \__/12\__/  \__/  \__/  \__/18\
>            __/ 4\__/  \__/  \__/  \__/  \__/
>         __/  \__/  \__/  \__/11\__/  \__/
>      __/  \__/  \__/  \__/12\__/18\__/
>     / 4\__/  \__/  \__/  \__/13\__/
>     \__/  \__/  \__/  \__/  \__/19\__
>        \__/  \__/12\__/  \__/  \__/  \__
>           \__/ 4\__/13\__/  \__/  \__/  \__
>              \__/14\__/  \__/  \__/  \__/19\
>            __/ 5\__/  \__/  \__/  \__/  \__/
>         __/  \__/  \__/  \__/13\__/  \__/
>      __/  \__/  \__/  \__/14\__/19\__/
>     / 5\__/  \__/  \__/  \__/15\__/
>     \__/  \__/  \__/  \__/  \__/20\__
>        \__/  \__/14\__/  \__/  \__/  \__
>           \__/ 5\__/15\__/  \__/  \__/  \__
>              \__/  \__/  \__/  \__/  \__/20\
>                       \__/  \__/  \__/  \__/
>                          \__/15\__/  \__/
>                             \__/20\__/
>                                \__/
> 
> 
> 
> 	I like this pretty well. Make enough hexes per triangle, and 
> the singularities hardly matter at all. But I'm not sure it works 
> with hex rows going north-south.
> 
> At 4:11 -0400 3/16/08, TFT Digest wrote:
> >1. Approximate Earth radius to say 6,360,000 meters.
> 
> 6,378,137 meters according to one model (a decade old or so, and the 
> last 3-4 digits change with every model) mean equatorial radius. Good 
> memory, PvK!
=====
Post to the entire list by writing to tft@brainiac.com.
Unsubscribe by mailing to majordomo@brainiac.com with the message body
"unsubscribe tft"