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I want to scale down the polyhedron by a given factor as shown below, where polyhedron is defined by $n_i(x-x_i) = 0, i=0,...,5$. That can be formulated as \begin{equation} P = \{ x \in \mathbb{R}^n \mid a_i^Tx \leq b_i, \; i=1,...,5\} \end{equation}

Any idea to achieve this is really appreciated enter image description here

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