States are political entities that incorporate within their established borders one or more nationalities. Each state can be categorized according to its physical characteristics, including its shape. Those categories include compact, fragmented, elongated, prorupted, and perforated, as well as other defining characteristics like the dominance of desert or major boundaries that run along large bodies of water (i.e., countries with long coastlines). In the cases of Nepal, Colombia, Nicaragua, Portugal and France, the categories, unsurprisingly, vary depending upon each state's shape. Portugal is categorized as an elongated state along with more obvious examples like Vietnam and Chile, which are long, slender territories. Nepal has been categorized as rectangular, but elongated is a more established term for countries of its shape, so that is where is it could be categorized for purposes of this exercise.

France would appear to be compact given that its center is relatively equidistant from its borders. It is, however, more properly categorized as fragmented because of its island territories in South America and the Caribbean, specifically, the territories of French Guyana and Corsica, which are physically detached from France "proper." Colombia is a prorupted state, as it combines the characteristics of a compact state with an extension in its northern-most provinces.

These countries are compact, the simplest shape. Compact states look basically like circles, with some minor variations. They are centered around a single geographic center which is often a political and economic center as well, and the rest of the country is defined by its proximity to that center. Poland and Germany are also compact states.

A prorupt state is like a compact state but with a long protrusion sticking out of it, like the pseudopod of an amoeba. These states often form in competition with others over some region of political or economic significance. Thailand is an example.

An elongated state is one that is very long and thin, often limited by terrain such as mountains or oceans. Panama and Chile are elongated states.

A fragmented state is one that is broken up into parts, so that there are some parts of the state between which there is no continuous land path that would connect those two parts. The United States was a compact state until we acquired Hawaii and then Alaska; now we are a fragmented state. Because they are fragments far from the center of the country, Alaska and Hawaii are known as exclaves.

Finally, a perforated state is just what it sounds like: A state with holes in it that are filled by other states. South Africa is perforated by Lesotho. The states that are surrounded by the perforated states are called enclaves.