The Vietoris–Rips complex is closely related to the Čech complex (or nerve) of a set of balls, which has a simplex for every finite subset of balls with nonempty intersection: in a geodesically convex space "Y", the Vietoris–Rips complex of any subspace "X" ⊂ "Y" for distance δ has the same points and edges as the Čech complex of the set of balls of radius δ/2 in "Y" that are centered at the points of "X". However, unlike the Čech complex, the Vietoris–Rips complex of "X" depends only on the intrinsic geometry of "X", and not on any embedding of "X" into some larger space.