Is one condition of Banakh spaces redundant?

Question

A Banakh space (not to be confused with Banach spaces) is a metric space $M$ such that all nonempty spheres of positive radius $r$ has cardinality $2$ and diameter $2r$. I am wondering if the second condition is redundant. Or is there a metric space such that all nonempty spheres of positive radius $r$ has cardinality $2$, but not all of them have diameter $2r$?

Answer 1

The condition is necessary, consider vertices of an equilateral triangle in the plane with sides $1$. Then all non-empty spheres have radius $1$, they have cardinality $2$, but their diameter is less than $2$ (it's in fact equal to $1$).