Planimetric Maps

http://www.nps.gov/history/history/online_books/fova/clr2-5c.htm

This here is a representation of a planimetric map because it only shows the horizontal aspects of the region, it does not take into consideration the vertical aspects as well, so therefore it does not express them.

Azimuthal Equidistant

http://www.acsu.buffalo.edu/~dbertuca/maps/cat/map-projections.html

This is a representation of an azimuthal map that is also equidistant. What this means is that it takes a spherical surface and places it on to a flat plane. This is possible by taking a flat plane that is tangent to the spherical surface so that contact is at a single point. Then if you were to look at the spherical surface that is encompassed through the flat plane, you have created an azimuthal projection. This example is also equidistant meaning that each point on the map is in true distance as it would be in reality and maintain their actual proportions to one another.

Mental Maps

http://www.fedstats.gov/kids/mapstats/concepts_mentalmaps.html

This is a representation of what appears to be a neighborhood that was drawn based off of the author's own memory. The interesting thing about mental maps is that no map is alike. Each map represents what that person sees as the unique qualities of that place and/or their own personal experiences there. Mental maps are directly in relation to an individual's own imagination and how they perceive someplace, so in a sense they are never truly wrong. Mental map's are also generally stored within the individuals mind, however in some cases, like seen above, they may be drawn out.