Dihedral angles of a simplex

2018-10-19 15:52:15

Given a $k$-simplex $(p_0, ..., p_k)$, where $p_i$ are $n$-dimensional points.

Define the dihedral angle $\theta_j$ as the angle between the (hyperplanes of the) two $(k-1)$-facets incident to the $(k-2)$-facet $e_j$, where $j \in 0, ..., \frac{n(n + 1)}{2} - 1$.

For a tetrahedron ($k = 3$), it means that the dihedral angle $\theta_j$ is the angle between the (planes of the) two faces incident to edge $e_j$, where $j \in 0, ..., 5$.

Now, what is the computationally simplest way to compute any of $\theta_j$?