  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). Assuming little familiarity with the subject, we give an
introduction to computations in polyhedral geometry using 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 left for experts in
polyhedral geometry. These are concerned with face numbers of random polytopes,
constructions and properties of Gelfand-Tsetlin polytopes, and secondary
polytopes.
