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On the AuthaGraph world map the world is mapped on a tetrahedron, so the map near the poles fits more the real sizes of the continents.

But isn't the north pole extremely deformed when projected on the peak of the tetrahedon?

AuthaGraph world map

It just doesn't look right, If you compare this:

AuthaGraph - Europe centered and North Pole with:

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    Talk to Authagraph or Hajime Harukawa as they have patents on the projection. That is, they would probably want payment for use.
    – mkennedy
    Commented Dec 9, 2016 at 18:33

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According to wikipedia the Authagraph is "an approximately equal-area world map projection" meaning sizes of regions are nearly true to scale. It also appears, to me, to keep shapes of regions, including both polar regions, reasonably true to form. Yes, the arctic circle gets squashed but note that all map projections introduce distortions of some kind. And distortion increases with distance away from the points or lines of contact (where the globe and the map coincide).

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  • Please note that for projections like this the concept of "points or lines of contact" makes no sense. This projection contains some heavy shape distortion--but the areas of such distortion have been concentrated near the north pole, the middles of the oceans, and a few other places (like the middle of South America). This can be seen by looking at the graticule: shape distortion is indicated wherever two lines that ought to be perpendicular are not perpendicular on the map. The graticule looks pretty good throughout most continental land masses.
    – whuber
    Commented Nov 9, 2016 at 18:50
  • So a Map where the south pole would be deformed would be interesting for Europeans: gis.stackexchange.com/questions/220889/…
    – rubo77
    Commented Dec 9, 2016 at 13:37
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According to people who attempted recreating the AuthaGraph projection, the map indeed have some distortion, but the trick is those distortion are limited to South Pacific, South Indian Ocean, South Atlantic, and the Siberia/North Pole area, and these area are mostly covered by ocean with little population, thus they can preserve the proportion of land on the map.

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