This is the simplest, plainest and probably the most obvious hexagonal neighbourhood imaginable. Previously this neighbourhood has been known as the "Uniform" neighbourhood (e.g. see [ the pages of Charles Herring]). It has also been called the "Hexagonal neighbourhood" e.g. [here]. This name seems too broad to me - as there are a large number of other hexagonal neighbourhoods. "Honeycomb" appears to be a superior name to (say) "graphite", as far as images of planes tesselated with hexagonal tiles go.
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