Datastructure

A multi-cell polyhedron \(\Gamma^{\perp}\) and its corresponding polyhedral form diagram \(\Gamma\) are modelled as volmesh and network, respectively. Because \(\Gamma^{\perp}\) and \(\Gamma\) are topologically dual to each other, \(\Gamma\) can also be modelled as a volmesh. However, because the topological information of \(\Gamma\) is embedded in \(\Gamma^{\perp}\), some information do not need to be duplicated. For example, the face and cell information of \(\Gamma\) can be computed from the topology of \(\Gamma^{\perp}\). The polyhedral form diagram \(\Gamma\) as a network is essentially a visualisation of the cell connectivity information of \(\Gamma^{\perp}\), where each edge of \(\Gamma\) is perpendicular to its corresponding face of \(\Gamma^{\perp}\).