Polytope
A polytope in halfspace representation is defined as
$$\mathcal{P} := \bigg\{ x \in \mathbb{R}^n \, \bigg| \, Ax \leq b \bigg\} . $$
A polytope in vertex representation is defined as
$$\mathcal{P} := \bigg\{ \sum_{i=1}^s \beta_i v_i \, \bigg| \, \sum_{i=1}^s \beta_i = 1, \beta_i \geq 0 \bigg\} . $$
Polytopes are convex sets.
More information in Section 2.2.1.4 in the CORA manual.