11-cell

11-cell
Rank	4
Type	Regular
Space	10-dimensional Euclidean space
Notation
Schläfli symbol	$\{\{3,5\}_5,\{5,3\}_5\}$
Elements
Cells	11 hemiicosahedra
Faces	55 triangles
Edges	55
Vertices	11
Vertex figure	Hemidodecahedron (5-dimensional)
Edge figure	Triangle
Related polytopes
Army	Ux
Regiment	Ux
Dual	11-cell
Convex hull	10-simplex
Abstract & topological properties
Flag count	660
Euler characteristic	0
Schläfli type	{3,5,3}
Orientable	No
Skeleton	K11
Properties
Symmetry	L2(11), order 660
History
Discovered by	Branko Grünbaum
First discovered	1976

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

Vertex coordinates

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

External links

• Wikipedia Contributors. "11-cell".
• Weisstein, Eric W. "11-Cell" at MathWorld.
• Hartley, Michael. "{3,5,3}*660".
• Klitzing, Richard. "11-cell"

Bibliography

• 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)