<p>There is a <a href="https://arxiv.org/pdf/1612.03467.pdf" rel="nofollow noreferrer">paper</a> which handles the case of equal area tiling (almost square tiles around the equator) and is relatively easy to pre-compute neighbouring tiles and on which tile a specific set of coordinates falls in. It doesn't fare well with the requirement for equal distance between the vertices though.</p>

<p>Copying here the abstract:</p>

<blockquote>
  <p>A  new  method  is  proposed  to  divide a spherical  surface  into  equal-area cells.  The method is based on dividing a sphere into several latitudinal bands of near-constant  span with further division of each band into equal-area cells.  It is simple in construction and provides more uniform latitude step between latitudinal bands than other methods of isolatitudinal equal-area tessellation of a spherical surface.</p>
</blockquote>

<p>(I've used its ideas trying to find closest geolocation neighbours from a long list of locations).</p>
Covering Earth with Hexagonal Map Tiles
<p>Many strategy games use hexagonal tiles.  One of the main advantages is that the distance between the center of any tile and all its neighboring tiles is the same.</p>

<p>I was wondering if anyone has any thoughts on marrying a hexagonal tile system with the traditional geographic system (longitude/latitude).  I think it would be interesting to cover a globe with hexagonal tiles and be able to map a geographic coordinate to a tile.</p>

<p>Has anyone seen anything remotely close to this before?</p>

<p><strong>UPDATE</strong></p>

<p>I'm looking for a way to subdivide the surface of a sphere so that each division has the same surface area.  Ideally, the centers of adjacent sub-divisions would be equidistant.</p>