An enclave is the name given to a state that is completely surrounded by another state. Famous examples of enclaves include Lesotho (which is completely surrounded by South Africa) and San Marino and Vatican City (which are completely surrounded by Italy).

A “landlocked state” is a state that is completely surrounded on all sides by other countries that has no direct access to the ocean. Of these countries, only Bolivia is landlocked state. Its access to the Pacific Ocean is blocked by the territory of Chile and Peru, something that has been the source of frequent war. Russia and Germany were two famous examples of landlocked states, but they both were able to expand to gain access to the ocean at some point in their history.

Italy is the classic example of a perforated state because it completely surrounds two other countries, San Marino and Vatican City. The name given to the region that is surrounded by the perforated state is an “enclave.” So San Marino and Vatican City are both enclaves within the perforated state of Italy.

A physical boundary is something tangible and concrete that is often used as the political barrier between two states. Mountain ranges and rivers are common examples of these throughout the world. A line of longitude, however, is a human construction, not a physical boundary. When a line of longitude or latitude is used to represent the political barrier between two states, this is known as a "geometric boundary."

Vatican City is an example of an enclave because it is an independent state that is completely surrounded by the borders of another state, in this case, Italy. Switzerland, although landlocked, is bordered by many countries and is thus not technically an “enclave.”

The Philippines is considered a fragmented state because its territory is physically divided, by the ocean, into several distinct regions that make it harder for a centralized government to wield control. Although the territories of the United Kingdom and the United States are not wholly contiguous they are not usually considered to be fragmented states because the vast majority of their significant territory is contiguous.

A compact state is a state that is reasonably small and centralized; it usually somewhat resembles a square. Compact states are usually easier for a centralized government to manage because every outlying region in the country is roughly equidistant from the center. Poland is the classic example of a compact state. The opposite of a compact state is an elongated state.

The term “annexation” is used to describe the internationally legal addition of new territory into an existing state. When we use the phrase “internationally legal” this is of course a dubious distinction, but essentially a nation can “annex” more territory in certain situations without it being considered an act of war. The United States, during its history of westward expansion, consistently annexed new territory, primarily because the Native Americans were not considered legitimate claimants to the land by the international community.