Rupert property of some solids in higher dimensions

We say that a solidS has the Rupert property if a hole could be cut into one copy of S so that another copy of S can be passed through this hole. In recent years, many solids in R$ have been shown to have the Rupert property. However, not much is known about the Rupert property in higher dimensions. This dissertation investigates the Rupert property for some solids in R". We introduce lemmas that help to verify this property. In particular, we prove that some particular n-simplices, the generalized n-octahedrons/and the two-way cones in In have the Rupert property.