Suppose that $A$ is a finite subset of $\mathbb{R}^d$ such t...

Prompt

Suppose that $A$ is a finite subset of $\mathbb{R}^d$ such that (a) every three distinct points in $A$ contain two points that are exactly at unit distance apart, and (b) the Euclidean norm of every point $v$ in $A$ satisfies \[\sqrt{\frac{1}{2}-\frac{1}{2\vert A\vert}} \le \|v\| \le \sqrt{\frac{1}{2}+\frac{1}{2\vert A\vert}}.\] Find the maximum cardinality of $A$ in terms of $D$.