As an example, consider the uniform metric space "M"3 consisting of three points, each at unit distance from each other. The Vietoris–Rips complex of "M"3, for δ = 1, includes a simplex for every subset of points in "M"3, including a triangle for "M"3 itself. If we embed "M"3 as an equilateral triangle in the Euclidean plane, then the Čech complex of the radius-1/2 balls centered at the points of "M"3 would contain all other simplexes of the Vietoris–Rips complex but would not contain this triangle, as there is no point of the plane contained in all three balls. However, if "M"3 is instead embedded into a metric space that contains a fourth point at distance 1/2 from each of the three points of "M"3, the Čech complex of the radius-1/2 balls in this space would contain the triangle. Thus, the Čech complex of fixed-radius balls centered at "M"3 differs depending on which larger space "M"3 might be embedded into, while the Vietoris–Rips complex remains unchanged.