^{[1]}etc.) tend to be based on population so have wildly differing geographic sizes depending on population density. This means that, if we plot a map based on those areas, the result will be hugely visually distorting because areas of high population density will appear very small on the resulting map even though they might be just as significant as much larger regions of very low population density. In a map of England, for example, central London looks very small but a lot of people live there; the whole county of Cumbria, where nobody seems to want to live, is huge but much less significant

^{[2]}. So, sometimes, we want to aggregate data on maps into areas of roughly equal area. This avoids the visual distortion inherent with statistical or governmental boundaries. Hexagons look like a good candidate for quick ad-hoc areas.

^{[3]}sort of hairy.

Applying these calculations on a dataset

^{[4]}for locations in england and wales generates this map (which exactly matches the hex centres in the first map above with hexagons with sides of 1 degree).

^{[5]}The hexagons are squashed along the x-axis. The problem arises from spherical geometry. Travelling a degree west from the centre of London takes you about 37km but travelling a degree north takes you 111km on the spherical surface of the earth. Visually the map doesn’t look that distorted because the effect is partially compensated for by the distortions inherent in the Mercator projection which stretches horizontal distances depending on latitude. But the compensation isn’t exact and the visual result varies by latitude. At least the distorted hexagons tessellate. It is beyond my brain’s ability to worry about whether the distance distortion is significant for analytic purposes but grappling with this is for another day. Besides, with a bit more spherical geometry we could compensate for this by applying different (latitude-dependent) scaling factors for the coordinates. But that, too, is for another day.

**do**have enough points but for some reason they don't plot. It is true that points with smaller numbers of original lat/lons tens to be the ones that don't plot but the actual reason why they don't plot is a bit of a mystery).

^{[6]}Hexes near the edge of the area have fewer than a handful of transactions (and therefore even fewer locations as each postcode may cover more than one house). They therefore don’t always have enough PointIDs to generate enough points to create the vertices for a complete hexagon.

PS My experimental workbook for the above examples is too big for Tableau Public so I can't link to it here. But I have a workbook that just uses the postcode locations (of which there are about 2.5m) that illustrates the way hex bins work. It is a little dull as the density of postcodes is basically an unreliable proxy for population density. But the workbook is here for those who want to check out the formulae or some simple analysis of how UK postcodes work.