I am trying figure out the minimum size of a world that is made of hexagonal tiles for it to be not very noticeable. I cannot find anything online that is directly helping me; so I come here. In my model, every hexagon is 10 meters in diameter.

enter image description here

Make a geodesic sphere with only hexagons.

The geodesic sphere

  • What is the minimum number of hexagons to produce this?
  • What is the minimum number of hexagons I need to add to make the geodesic sphere larger?
  • How do I calculate the angle of declination given the number of hexagons in a geodesic sphere?

There are the questions I have come up with. Let me know if they need to be on their own question, but they are all closely related to each-other.

Any help on this is much appreciated.

Thank you

  • 5
    $\begingroup$ If you look closely enough at the image you linked, you will notice several pentagons :-) In fact, it is not possible to build a sphere using only regular hexagons. $\endgroup$ – tristan Jul 23 '17 at 0:32
  • 2
    $\begingroup$ nooooooooooooooo! $\endgroup$ – Tsangares Jul 23 '17 at 0:41
  • $\begingroup$ ill look into triangles. $\endgroup$ – Tsangares Jul 23 '17 at 0:42
  • 2
    $\begingroup$ Yes, you need pentagons, 12 of them, or smaller numbers of squares or triangles. But try using hexagons to tile a torus. $\endgroup$ – Oscar Lanzi Jul 23 '17 at 0:44
  • $\begingroup$ That is an interesting proposal, a toroidal world. $\endgroup$ – Tsangares Jul 23 '17 at 0:53

"ill look into triangles"


  • $\begingroup$ Is each triangle in this the same size? $\endgroup$ – Tsangares Jul 24 '17 at 5:17
  • 1
    $\begingroup$ @Tsangares: Nearly but not precisely. It is not possible to tile the sphere with many equilateral triangles. This is about as close as is achievable. $\endgroup$ – Joseph O'Rourke Jul 24 '17 at 11:48

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