Triangles in Space or Building and Analyzing Castles in the Air Classic Reprint

Excerpt from Triangles in Space or Building (and Analyzing) Castles in the Air

At various points in our analysis we will have to consider planar arrangements of segments which are similar to the 3-dimensional case, partitions of a plane into faces, edges, and vertices induced by a collection of segments in that plane. As a bounded face of such an arrangement need not be simply connected, its boundary will in general consist of a single outer component that encloses the entire face and zero or more islands each enclosing a portion of the plane that does not belong to the face. An unbounded face has a similar structure, except its boundary does not have anouter component.

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