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
Famous quotes containing the words face and/or arrangement:
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—Maurice Blanchot (b. 1907)
“There is no reason why parents who work hard at a job to support a family, who nurture children during the hours at home, and who have searched for and selected the best [daycare] arrangement possible for their children need to feel anxious and guilty. It almost seems as if our culture wants parents to experience these negative feelings.”
—Gwen Morgan (20th century)