P.S. @ Zompa: I'm posting all these works of your on your behalf; I hope you've nothing against this. Otherwise, let me know!
No problem at all: as soon as they are on the web, I consider them as public: feel free to post and use them as you like
...in another topic LoZompatore demonstrated that the "darklands" between outer and hollow world aren't that "dark" nor so "cold" (most of the area receives light from at least ONE sun, and a small portion of it even light from both suns - I mean, the real sun and HW sun)...
The link to the italian topic Zendrolion posted above was an attempt to give a realistic description of what would happen in the polar openings as they are lit by the external sun. Moreover, I tought it was cool to have a very strange habitat in the middle of the stormy/icy area of the opening: the climate would be "interesting" indeed: on some regions in the middle of the opening you'll have 6 months of tropical/equatorial climate (when the emisphere is in summer) and 6 months of polar climate (when the emisphere is in winter).
The ecosystem would be strange indeed (what about this area hosting some altered plants and animals created by the Immortals just after the GRoF, when the climate patterns were so upset that the Immortals had to create special living beings - able to survive to sudden and impredictable cold and hot periods - in order to provide enough food for the starving populations of some areas.
If you like I can translate the whole topic and send it in the Hollow World section. It is not official, but is interesting anyway.
(EDIT: the topic above is done: you'll find it in the Hollow World section of the message board
Now, about the Pentagon/Hexeagon fix:
The Pentagon/Icosahedron fix for the distortion is brilliant (I'd never even considered that things would distort at the poles)
As you may guess this solution is not mine, but it comes from some mathematic property concerning the geode and the tessellation of a sphere. Moreover, it is also geometrically possible to hexmap the torus (the donut) without distortions so, in principle, we might also have a proper hexagonal mapping for the polar opening area (which is half a torus in shape). This is not an easy task, though.
Something just occurred to me about our icosahedron fix: doesn't this mean that we're going to want to have our hexes with a point to the north, as opposed to with a flat face to the north? Looking at LoZompatore's excellent icosahedron globe, it really seems like there's going to be no way around this, and no way to keep the flat faces to the north.
You are absolutely right. There is no chance to rotate the hexes in such a way you can have the flat side of the hexes in the WE direction instead of having them NS.
The only possible solution I found is described below:
Let's call the hexes of the icosahedron gridding I posted above a "vertical" hex (it has the flat side in the NS direction). The standard Mystara hexes are instead the "horizontal" hexes(the flat side is in the WE direction).
- We may use just the icosahedron frame of "vertical" hexes as a reference for the global map, in order to take in account for latitude distortions and the like. The scale of the "vertical" hexes is not important as they just give the border of the map we want to fill.
- We may fill each "vertical" hex with the standard "horizontal" hexagonal grid of the Mystara's maps we know.
To give you a visual idea of what I'm saying:
http://it.geocities.com/lutetius00/Hexa ... _small.jpg
The bigger hexes give just the frame of the map (the single hex borders dont'even need to be represented in the map, except for the ones composing the side of the icosahedron face), while the smaller hexes represents the standard Mystara map.
Of course you are assuming that the bigger hexes are flat surfaces, and you are introducing an error in area and distance evaluations especially at the center of the bigger hex, but this error is quite small compared to the one we have without taking into acocunt the latitude distortion (that is pretty much avoided with an icosahedral map).
My big question (being a pen, pencil, and paper guy) is........."Where can I find this neat hex paper with the pentagons every so often?"
If you are referring to the blank map I posted above, I made it with some patience. Maybe I have also the hexed verion of it (with hexes inside the blank area, instead of having also the borders), if you are interested I can place it on the web. Unlukily I do not have other bigger/smaller resolution maps.
Zompatore is a God!
Ahahahah! Actually I'm just doing my Immortal Path in the Sphere of Tought...
Icosahedron planet mapping in the standard that was used in the Traveller RPG, and later for GURPS:Space. You can find some utility programs for them here
Cool! Thank you! I've never heard of them before!