I'm trying to figure out
(1) what this type of map linked here is called (I've been unable to find the name through search), and
(2) whether there is an Arc tool that will transform a shapefile or feature class with geospatially referenced polygons into a map like this where the relative spatial positions of the polygons are preserved, but the areas are equal and the shapes are transformed?
Best Answer
(1) I have usually heard of it referred to as a "Hexagonal Map" or "Hexagonal Grid Map". Both queries turn up a lot of relevant results in Google. Example Link Here: http://anitagraser.com/2012/03/04/mapping-density-with-hexagonal-grids/
The link above also outlines the process that you would use in QGIS.
If you want to do it in ArcGIS. This article from the ESRI blog offers some insight into the flow in model builder and also a link to the geoprocessing package you can download. Package Link Here