In the Chapter 2 of Convex Optimization by Boyd and Vandenberghe. The definition of a polyhedron is as follows:
A polyhedron is defined as the solution set of a finite number of linear equalities and inequalities : $$\mathcal P = \{x : a_j^Tx\leqslant b_j, j=1,\ldots,m, c_j^Tx=d_j, j=1,\ldots,p\}. $$
But in the example shown in Fig. 2.11, shown as follows: 
I could not find where the hyper planes (i.e., equations) are, and thus I could not understand the function of equations here. Why equations are needed to define a polyhedron?
The Figure 2.11 shows an example where $p=0$, i.e., there are no equations $c_j^Tx=d_j$.
If $p\geq1$ then the equations $c_j^T=d_j$ $\>(1\leq j\leq p)$ define an affine subspace $V$ of ${\mathbb R}^n$, in general of dimension $n-p$. For the given problem only the points $x\in V$ are interesting. It would be possible to choose new coordinates $y_k$ in such a way that $V={\mathbb R}^{n-p}$. The inequalities $a_j^Tx\leq b_j$ $\>(1\leq j\leq m)$ would then be transcribed into inequalities in terms of the $y_k$, and we are in the situation of Figure 2.11.