Simplicial Surfaces
Ethan D. Bloch · Birkhäuser Boston eBooks · 1997
Topological surfaces can sit in Euclidean space very wildly, and as such can be difficult to work with. In order to develop the tools necessary for our proof of the classification of surfaces, as well as for other results, we turn our attention to simplicial surfaces, which are surfaces built out of triangles, and which are much easier to work with than arbitrary surfaces. Examples of simplicial surfaces include the surface of a tetrahedron (a pyramid with a triangular base) or an octahedron. See Figure 3.1.1. Simplicial surfaces have two advantages: They cannot sit wildly in Euclidean space, and they have things we can count (for example, the number of vertices) and measure (for example, angles).