Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!

While stated previously I can't necesarily give you specific reason why there are no 3-sided pyramids, I can give you a few general points of interest that may help on why there are 4-sided pyramids.

The Great pyramid is probably the most famous of all of the ancient egyptian pyramids and as all of the others is 4 sided (althought contrary to popular belief it actually is 8-sided, which can be seen from aeriel photographs). The Great Pyramid is surpising well aligned with the cardinal points on a compass, that being north, south, east and west, which would suggest that it was purposefully done, if this is true it would stand to reason that the four sides would be necessary to face each direction.

Linguistically and culturally humans like using four general directions, forward, backwards, left, right. There are a few lanuagues that even use the cardinal directions instead of general directions, this is generally why people all around the world build structures with four walls.

The last general point to make regarding pyramids would be a popular theory on how they were built, 3D scans seem to suggest that the pyramids were built using spiraling ramps up the side of the pyramids. (Imagery of Cheops Pyramid showing ramps) ("Imaging the Cheops Pyramid" by Bui, H.D. 2012). If you were to attempting using this building method with a three sided pyramid you would be forced to make a 120 degree turn, instead of a 90 degree turn, which for obvious reason would be much more difficult.

​

I hope these quick general points help point you towards why four sided pyramids are the norm.

​