Figure 3.

Illustration of simplicial complexes. The tetrahedron-shaped simplicial complexes are depicted in a₁ to a₃, and the cube-shaped simplicial complexes are demonstrated in b₁ to b₃. In each shape, the leftmost simplicial complex has only 0-simplexes and 1-simplexes. As filtration processes, 2-simplexes emerge in the middle one. In the final stage, a 3-simplex is generated. Table 1 gives a description in terms of vertices, edges, faces and cells.