Polyhedral Geometry in OSCAR

OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number theory). Here, we give an introduction to polyhedral geometry computations in OSCAR, as a chapter of the upcoming OSCAR book. In particular, we define polytopes, polyhedra, and polyhedral fans, and we give a brief overview about computing convex hulls and solving linear programs. Three detailed case studies are concerned with face numbers of random polytopes, constructions and properties of Gelfand-Tsetlin polytopes, and secondary polytopes.