There are many different types of roofs. The most common roof, and the archetype we often picture, is the gable roof. The gable roof is made up of two right triangles and slopes on two sides. A shed roof is even more basic: it is made of 1 right triangle and slopes on one side. A hip roof is slightly more dynamic roof with four slopes (see illustration). Four hip rafters brace the roof making it sturdier, and more difficult to construct, than a gable roof. (Koel: p.336) There are different combination roof styles you can make with these three roofs. There is the butterfly shed*, the monitor shed, and the continuous slope gable, to name a few.
basic types of roofs
Besides the three basic roof types (gable, shed and hip) there are also gambrel and mansard roofs. Gambrel roofs have a double-slope on each side and are often what we picture as barn roofs. The advantage to a gambrel roof is the space directly under the roof (be it the attic or the 2nd floor) is larger. There is not a steep pitch cutting into the room. A mansard roof is similar to a gambrel but has the additional slopes like a hip roof. (Koel: p.336-337)
*Looking at the design, you may ask: why make a butterfly roof? In a place like Maine, it may not make sense to have a design that would fill up with snow in the winter. However, in other climates, especially places that have less rainfall, a butterfly roof can be used to collect rain water. Butterfly roofs were also used to give a home or building a modern look.
1. Koel, Leonard: Carpentry, Third Edition. Copyright 1997 by American Technical Publishers, Inc.