The Pyramid Vertex Module (PVM) is actually a family of units. It consists of vertex units which look like trigonal pyramids (hence the name) and connector units which are used to connect the vertex units. Different combinations of vertex units and connector units result in different models, sometimes as different as to not be obvious that they are built from very similar modules.
Vertex modules are very paper-efficient. In most places, there is only a single layer of paper, and the finished units are quite large relative to paper size. They can be folded from standard paper, but using somewhat thicker paper can make them more sturdy. Connector units, in contrast, have quite many layers and will not work well if folded from paper which is too thick.
After publishing this unit, I learned about a similar design (Polyhedron Construction Kit), by Miyuki Kawamura. Superficially, her design and mine are very similar (especially the Large Cube), but I believe my design to be superior: the triangular units are more paper-effective than Kawamura’s and the rectangular edge units (connectors) are thinner which makes the interior of the model more spacious and gives it a lighter appearance.