11-cell

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11-cell
Rank4
Dimension10
TypeRegular
Notation
Schläfli symbol
Elements
Cells11 hemiicosahedra
Faces55 triangles
Edges55
Vertices11
Vertex figureHemidodecahedron (9-dimensional)
Edge figureTriangle
Related polytopes
ArmyUx
RegimentUx
Dual11-cell
Petrie dual11-cell
Convex hull10-simplex
Abstract & topological properties
Flag count660
Euler characteristic0
Schläfli type{3,5,3}
OrientableNo
SkeletonK11
Properties
SymmetryL2(11), order 660
History
Discovered byBranko Grünbaum
First discovered1976

The 11-cell, or hendecachoron, is an abstract regular polychoron and regular skew polychoron in 10-dimensional Euclidean space. It has 11 hemiicosahedral cells. It is self-Petrial.

Vertex coordinates[edit | edit source]

The vertex coordinates of the 11-cell are the same as those of the 10-simplex.

External links[edit | edit source]

Bibliography[edit | edit source]

  • Grünbaum, Branko (1976). "Regularity of Graphs, Complexes and Designs" (PDF). Problèms Combinatoire et Théorie Theorie des Graphes (260): 191–197.
  • Séquin, Carlo (2012), A 10-Dimensional Jewel (PDF)