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In this approach, we represent the cube by providing a list of all vertices and all edges (as represented by pairs of vertices). Are there ever situations where it would be computationally advantageous to provide an alternate representation, perhaps a more abstract one?


Are there general assumptions about the faces that connect the edges (as applied to situations that could be more complex than a simple cube), like that they are flat and connect the closest closed shape of edges and whether or not they exist between certain edges at all?


When modeling in 3D software, there is big emphasis on faces, so would it make sense to represent the cube in terms of its faces instead of edges?


This algorithm requires the edges and the endpoints to model the cube. How might one model a cube that has curvature and no edges?