Dove's Foot Cranesbill
Geranium molle
Dove's-foot Crane's-bill is also rendered Dovesfoot Cranesbill, aka Dove's-foot Geranium. It is Geranium molle, originally a European wildflower, but so long naturalized in the United States it is found from coast to coast.
The flowers of Dove's-foot Crane's-bill look like teency pink ten-petalled lilac-pink daisies, but if you look closely, they have "obdurate petals" meaning each petal looks like two, & if you plucked one of these petals, it is heart-shaped; there are really only five of these petals per flower. The name Crane's-bill or Cranesbill is derived from the fact that the pistil & calyx, once the flowers are spent, look like the heads of cranes. Erodiums are called "Storkesbill" for the same reason.
People who want perfect lawns that look more like astroturf than anything alive will never tolerate this "nasty weed" because it easily spreads into turf, keeping its leaves low to evade being too mowed down. But it is sometimes offered in nursery catalogs, particularly by wildflower specialists (although given its ubiquity I would recommend just taking one from a roadside or ditch, or save & care for one that is already in the yard). Whoever delights in species wildflowers will be rewarded by feeding & encouraging a couple of these, discovering thereby the extreme edge of their beauty which is hardly less than any cultivar cranesbill.