Figure 1

Illustration of constructions of (a) Discrete Dirac matrix \(\textbf{D}_1\) of a triangle and (b) Discrete Dirac matrix \(\textbf{D}_2\) of a tetrahedron along with its corresponding boundary matrices. The rows and columns of boundary matrices corresponds to a respective simplex each. For instance, in the boundary matrix \(\textbf{B}_2\) of (a), edge \(e_{12}\) is oriented similarly as \(t_{123}\), hence having an entry 1 in the matrix. As the entries of Dirac operator either take a value of \(-1\), 0 or 1, the entries of Dirac operators are color coded with blue indicating 1, white indicating 0 and red indicating \(-1\).