Theorem 34.4:

(i) The diameter of an affine $p-$simplex $\sigma = [{\bf v}_1, {\bf v}_2,\dots, {\bf v}_{p+1}]$ is the length of its longest side namely,

$$\max_{i \neq j}\Vert{\bf v}_i - {\bf v}_j\Vert.$$

(ii) The diameter of any constituent simplex in the chain $B\sigma$ is $${\Big(\frac{p}{p+1}\Big)\mbox{diam}\;(\sigma). }$$