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Isometries

There are many lower symmetry forms of the 5-cell, including these found as uniform polytope vertex figures:

The tetrahedral pyramid is a special case of a 5-cell, a polyhedral pyramid, constructed as a regular tetrahedron base in a 3-space hyperplane, and an apex point above the hyperplane. The four sides of the pyramid are made of triangular pyramid cells.

Many uniform 5-polytopes have tetrahedral pyramid vertex figures with Schläfli symbols ()∨{3,3}.

Other uniform 5-polytopes have irregular 5-cell vertex figures. The symmetry of a vertex figure of a uniform polytope is represented by removing the ringed nodes of the Coxeter diagram.