http://www.cleverscampcamp.com/camping-merit-badge-tent/

what are the four different kinds of tents?
I need to know for a Camping merit badge in Boy Scouts
Well, from what I found there are more than four basic designs–and many hybrids from those. You’ll have to do a little of the work yourself I guess. The first four listed are the 4 basic though, I believe:
Dome Tents
Three or more intersecting hoops with the Tent cover form a multi-faceted ground floor with a dome. The added hoops give this tent increased strength in comparison to Wedge Tents. However, they are mostly pretty difficult to erect. Most 4-Season tents are domes with four intersecting hoops.
Wedge Tents
Two intersecting hoops with the Tent cover form a square to round pocket. These tents are very popular in Hiking as they combine great strength in combination with the least use of material and weight.
Traditional A-Frame Tents
Two-legged frames at the outer ends of the Tent with the Tent cover form a triangular pocket. Old backpacking tents were often A-frame Tents. The increased roominess of hoop tents and domes has replaced most A-frame tents.
Pyramid Tents
One central pole and the Tent cover pulled tight and spread out around the center pole form a pyramid shaped pocket. Pyramid Tents are rare in Hiking as the center pole effectively divides the Tent in multiple smaller compartments.
Avian Tents
One or two straight poles with the Tent cover spread out create a covered ground area. They are mostly used for quick shelter and generally light weather conditions.
Hoop Tents
Use one to three hoops with the Tent cover to form a tubular pocket. The curved walls give a bigger volume with the same ground surface. Hoop Tents are surprisingly strong as they divide pressure over the full length of the hoops.
Trail to Eagle