Strongly Regular Graphs that are Locally a Disjoint Union of Hexagons

We prove that there are precisely two srg(64, 18, 2, 6) that are locally a disjoint union of three hexagons and there are no srg(40, 12, 2, 4) that are locally a disjoint union of two hexagons. As a side result, we obtain simple definitions for all 11 srg(64, 18, 2, 6) that are 4-colorable.