4-polytopes can also have the same face arrangement which means they have similar vertex, edge, and face arrangements, but may differ in their cells.
For example, of the ten nonconvex regular Schläfli-Hess polychora, there are only 7 unique face arrangements.
For example the grand stellated 120-cell and great stellated 120-cell, both with pentagrammic faces, appear visually indistinguishable without a representation of their cells:
Grand stellated 120-cell (120 small stellated dodecahedra) |
Great stellated 120-cell (120 great stellated dodecahedra) |
Read more about this topic: Vertex Arrangement
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