The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional space because its boundary cells are single-sided manifolds such as a Möbius strip or Klein bottle (Séquin and Hamlin 2007). Its 11 facets are hemi-icosahedra, and the vertex figure at each of its 11 vertices is a hemi-dodecahedron (Leemans and Schulte 2007).
11-Cell
See also
16-Cell, 24-Cell, 57-Cell, 120-Cell, 600-Cell, Hemi-Dodecahedron, Hemi-Icosahedron, Pentatope, TesseractExplore with Wolfram|Alpha
References
Grünbaum, B. "Regularity of Graphs, Complexes and Designs." Colloque Intern. C.N.R.S. 260, 191-197, 1977.Lanier, J. "Jaron's World: Shapes in Other Dimensions." Discover Mag., pp. 28-29, Apr. 2007.Leemans, D. and Schulte, E. "Groups of Type
Acting on Polytopes." Adv.
Geom. 7, 529-539, 2007. https://doi.org/10.1515/ADVGEOM.2007.031.Séquin,
C. H. and Hamlin, J. F. "The Regular 4-Dimensional 57-Cell."
International Conference on Computer Graphics and Interactive Techniques: ACM
SIGGRAPH 2007 Sketches. New York: ACM, 2007.Referenced on Wolfram|Alpha
11-CellCite this as:
Weisstein, Eric W. "11-Cell." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/11-Cell.html