There are many ways to represent a mesh.  The differences exist in the mesh connectivity.

The most basic representation is triangle soup.

• Separate triangles, each with its own three vertices
• No need to explicitly model triangles – implied by every three vertices

Triangle soup simply stores triplets of vertices in memory.  Every three vertices represent a triangle.

This approach is exceedingly simple, but has some disadvantages:

• Many vertices are repeated.  Typically, there are an average of ~2 triangles per vertex, so on average, each vertex is stored in memory twice.
• For a given triangle, it is not convenient to find neighbouring triangles or vertices. 
• Trying to search for matching vertices may be tricky due to floating point inaccuracy

High

Exercise:
How would you find the 1-ring neighbour faces of v0?