"Triangles", tetragons, 4-sided pyramid, these all describe the same thing: the simplest brush you have avaialable to build stuff with, most commonly describes as "triangles" in the forums.
NOTE: sometimes it is only necessary to clip a rectangualr brush into two triangles to make an "invalid solid" error and others go away, but sometimes if you have avery difficult shape, you are better off using purely tetragons or "triangles".
It is nearly impossible to get errors VMing with only these brushes. (clipping is another story of course).
To avoid the dreaded "leaf saw" errors on your during VIS Compile, construct your complex detail items and props in hammer entirely out of 4-sided polygons.
Included are a cube cut into 6, 4-sided polygons, and a partially hollow cube created out of 4, 4-sided polygons, slightly contorted.
I would recommend using only the first mentioned, 6-piece cube for your construction, as the weirdly hollow, 4-piece cube is more of a novelty, just showing you it's possible. However, if you can find a use for the 4-piece cube, go ahead!
Hope this helps some people endeavoring to create fancy brushwork in Valve Hammer Editor! Again, DO NOT make your entire map out of these stuctures! Doing so would be highly impractical/unnecessary, and boost your compile time to a unmanageable level very quickly..