Perfectly Repeating Square Grid on a Hexagonal Tile Base

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I am attempting to discover what the sizing ratios of squares and hexagons are. What I want to do with this information is determine (if possible) what size squares in a grid I should place over a hexagonal tiled floor so that the grid repeats correctly per tile with each hex tile having an identical segment of the square grid pattern imprinted on it. Essentially, the hexagonal tiles should be identical (including whatever portion of square grid), but when put together should display a complete square grid that would be imprinted onto the tiles.