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:
“In the long, sleepless watches of the night,
A gentle face—the face of one long dead—
Looks at me from the wall,”
—Henry Wadsworth Longfellow (1809–1882)
“The best protection parents can have against the nightmare of a daycare arrangement where someone might hurt their child is to choose a place that encourages parents to drop in at any time and that facilitates communication among parents using the program. If parents are free to drop in and if they exercise this right, it is not likely that adults in that place are behaving in ways that harm children.”
—Gwen Morgan (20th century)