没有五边形的球体上的六边形网格 [英] Hexagon grid on sphere without pentagon

问题描述

我想在一个球体上创建一个基于图块的世界.我想使用六边形的瓷砖，尽管据我所知，您也需要在其中放置五边形以使其适合.

I wanted to make a tile-based world on a sphere. I would like to use hexagon-shaped tiles, though as far as I can figure out you need to have pentagons in there too to make it fit.

所以，我的问题是，有可能在不使用五边形的情况下在球面上制作六边形网格吗?六边形不必一定是正六边形，如果它们都接近正则就足够了.

So, my question is, is it possible to make a hexagon grid on a sphere, without using pentagons? The hexagons don't have to be regular hexagons, if they are all close to regular that's more than enough.

推荐答案

不可能.这是数学定理.我猜只有不精确的方式存在.

Impossible. This is mathemetical theorem. Only imprecise ways exist I guess.

http://en.wikipedia.org/wiki/Platonic_solid

http://en.wikipedia.org/wiki/Semiregular_polyhedron

用六角形地图瓷砖覆盖地球

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