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Something very remarkable connects the following eight geographic places.
What is it?

  • Bodaybo (Russia)
  • Cape Horn
  • Christchurch (New Zealand)
  • Cocos Islands
  • Ghanzi (Botswana)
  • Honolulu
  • Punta Peclas (Nicaragua)
  • Vigo (Spain)
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    $\begingroup$ Guess: they form a regular octagon on a world map? $\endgroup$
    – Rand al'Thor
    Commented Feb 22, 2015 at 17:07

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The answer is:

These eight locations (roughly) form the vertices of a cube.

These eight places clearly are very far away from each other. They actually form four pairs of antipodal points (see for instance http://wikimapia.org/15392887/Antipodal-Point-from-Honolulu-Hawaii):

  • Honolulu and Ghanzi are antipodal
  • Punta Peclas and Cocos Islands are antipodal
  • Vigo and Christchurch are antipodal
  • Cape Horn and Bodabyo are antipodal

These eight points however do not maximize the minimum distance among all sets of eight points on the surface of Earth (which was my first guess). The maximizing point set would form the corners of a square antiprism with edges of equal length, and would not contain any pair of antipodal points:
http://mathworld.wolfram.com/SphericalCode.html
http://mathworld.wolfram.com/SquareAntiprism.html

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    $\begingroup$ Wow, nice! I was close then. $\endgroup$
    – Rand al'Thor
    Commented Mar 7, 2015 at 10:49

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