Constrained Hyperplane
A constrained hyperplane is defined as
$$\mathcal{CH} := \{ x \in \mathbb{R}^n \, | \, c^\top x = d, Ax \leq b \}, \quad c \in \mathbb{R}^n, d \in \mathbb{R}, A \in \mathbb{R}^{m \times n}, b \in \mathbb{R}^m . $$
Constrained hyperplanes are closed, convex and degenerate sets.
More information in Section 2.2.2.1 in the CORA manual.