From a gameplay perspective only the number or distance in tiles is really important, not the area of the tiles. The distance-in-tiles around the equator and around the poles is equal (216 tiles each, highlighted in yellow ).

At 45° to each of the six poles another six circles are highlighted in cyan . Note that for perfect symmetry one would have to highlight three instead of two neighboring lines of hexagons along the cyan paths (compare the North Pole detail image following in my next post); here I highlighted only two of them in order to show a path a unit could follow. Due to this slight asymmetry the unit does not travel along an exactly straight line; this geometric effect amounts to 218 tiles around the globe for the cyan circles instead of 216:

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circles square intersection view:

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circles triangle intersection view:

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circles diamond intersection view:

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