the.com/flagstone

A rock that gave up being a mountain to become a patio.

means A flat slab of stone, usually sedimentary rock like sandstone or slate, cut or split for paving floors, walks, and patios.

from From 'flag,' an old word for a slab of stone used for paving — itself borrowed from a Scandinavian source like Old Norse 'flaga,' meaning a slab or flat piece of stone or turf. It has no relation to the flag you wave; this flag was lying down long before any were run up a pole. 'Stone' was tacked on later simply to make the meaning unmistakable.

etymology
from flag meaning turf slab, not banners
cutting style
split along natural layers, not sawn
material range
sandstone, slate, limestone, quartzite all qualify
irregular shapes
prized precisely because no two match
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