Why is the vertical spacing between hexagon rows the height times 3/4?
Because pointy-top hexagons partly nest into each other: the top point of a hexagon in the row below slides into the gap left by the bottom point of the hexagon in the row above, and that overlap consumes exactly one quarter of the total height, leaving 3/4 as the effective distance between centers.
What hexagon radius works best so the background does not feel heavy?
For background texture behind text, a radius between 24px and 40px usually balances brand presence with restraint; above 64px the hexagon already dominates the composition visually and works better as an isolated decorative element than as a full-page texture.
Is the horizontal offset between alternating rows always half the width?
Yes, for the pointed fit to work: with a 55.4px width on a 32px radius hexagon, the offset has to be exactly 27.7px, because any other value makes one row's vertex fall outside the previous row's gap and opens a visible seam.
Does a flat-top hexagon use the same spacing formula?
Not with the roles unchanged: on a flat-top hexagon, the width plays the role the height played on the pointy-top version, times 3/4, while the height becomes what the width was; switching orientation means recalculating which dimension carries that 3/4 factor.