I reckon that Spherical triangulation of monthly global temperatures is by far the most honest way to present temperature data, but it has one drawback. You cannot make annual or longterm averages because the triangular mesh is forever changing from one month to another. To make such averages you really need a fixed grid. So does that mean that we have to give up and return to 2D fixed lat,lon grids such as those used by CRU, NOAA or NASA, in order to calculate annual distributions? The answer is no because there is a neat method of defining fixed 3D grids that maintains spherical symmetry. This is based on subdividing an Icosahedron.
Figure 1. shows the annual average temperature anomalies for 2016 using this method, while here and below is the WebGL (Nick Stokes) 3D interface.
An Icosahedron is a 20 sided object whose sides are equilateral triangles. The mesh is formed by dividing each triangle into 4 new triangles whose vertices are made to lie on a sphere. By repeating this procedure iteratively you generate an equal area mesh over the earth’s surface.
I was lucky to find an IDL package to do this, and after quite a struggle managed to integrate it with the global temperature data. I am using a level-4 mesh containing 2562 triangles which seems to be the best fit to the average density of global temperature measurements. Despite this there are still 94 empty triangles lying in remote regions. These have been assigned zero anomaly and are visible as occasional single light blue triangles.
Another well known way to tesselate a sphere uses hexagons, as on a soccer ball. However it turns out that this is a just a truncated icosahedron! Check out cutting off each vertex midway. It is just easier to make soccer balls that way.