page_title: Runcinated 5-cell
section_title: Full snub 5-cell
hierarchical_section_title: Runcinated 5-cell / Omnitruncated 5-cell / Full snub 5-cell
caption_attribution_description: English: Snub 5-cell vertex figure
context_page_description: In four-dimensional geometry, a runcinated 5-cell is a convex uniform 4-polytope, being a runcination of the regular 5-cell.
  There are 3 unique degrees of runcinations of the 5-cell, including with permutations, truncations, and cantellations.
context_section_description: The full snub 5-cell or omnisnub 5-cell, defined as an alternation of the omnitruncated 5-cell, cannot be made uniform, but it can be given Coxeter diagram , and symmetry [[3,3,3]]⁺, order 120, and constructed from 90 cells: 10 icosahedrons, 20 octahedrons, and 60 tetrahedrons filling the gaps at the deleted vertices. It has 300 faces (triangles), 270 edges, and 60 vertices.
  Topologically, under its highest symmetry, [[3,3,3]]⁺, the 10 icosahedra have T (chiral tetrahedral) symmetry, while the 20 octahedra have D₃ symmetry and the 60 tetrahedra have C₂ symmetry.
caption: Vertex figure for the omnisnub 5-cell
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