History of Use
Stereolithography machines are basically 3D printers that can build any volume shape as a series of slices. Ultimately these machines require a series of closed 2D contours that are filled in with solidified material as the layers are fused together.
The natural file format for such a machine would be a series of closed polygons corresponding to different Z-values. However, since it's possible to vary the layer thicknesses for a faster though less precise build, it seemed easier to define the model to be built as a closed polyhedron that could be sliced at the necessary horizontal levels.
The STL file format appears capable of defining a polyhedron with any polygonal facet, but in practice it's only ever used for triangles, which means that much of the syntax of the ASCII protocol is superfluous.
STL files are supposed to be closed and connected like a combinatorial surface, where every edge is part of exactly two triangles, and not self-intersecting. Since the syntax does not enforce this property, it can be ignored for applications where the closedness doesn't matter.
The closedness only matters insofar as the software which slices the triangles requires it to ensure that the resulting 2D polygons are closed. Sometimes such software can be written to clean up small discrepancies by moving endpoints of edges that are close together so that they coincide. The results are not predictable, but it is often sufficient to get the job done.
Read more about this topic: STL (file Format)
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