Theorem 34.1:

The boundary of the cone $K_{\bf b}\sigma = [{\bf b}, {\bf v}_1, {\bf v}_2,\dots, {\bf v}_{p+1}]$ is given by

$$\partial K_{\bf b}\sigma = \sigma - K_{\bf b}\partial \sigma \eqno(34.3)$$

Hitherto the choice of the apex ${\bf b}$ of the cone was arbitrary but now we shall specialize it to be the barycenter of $[{\bf v}_1, {\bf v}_2,\dots, {\bf v}_{p+1}]$ that we now define.