Overview
- Group
- SmallGroup(660,13)
- Rank
- 4
- Schläfli Type
- {3,5,3}
- Vertices, edges, …
- 11, 55, 55, 11
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 5
- Also known as
- 11-cell, {{3,5}5,{5,3}5}. if this polytope has another name.
Special Properties
- Universal
- Locally Projective
- Non-Orientable
- Self-Dual
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3,11)( 4, 7)( 5, 6)( 8,10);; s1 := ( 3, 4)( 5, 9)( 7, 8)(10,11);; s2 := ( 2, 9)( 4, 5)( 6, 7)( 8,10);; s3 := ( 1, 2)( 3, 4)( 7,11)( 8,10);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(11)!( 3,11)( 4, 7)( 5, 6)( 8,10); s1 := Sym(11)!( 3, 4)( 5, 9)( 7, 8)(10,11); s2 := Sym(11)!( 2, 9)( 4, 5)( 6, 7)( 8,10); s3 := Sym(11)!( 1, 2)( 3, 4)( 7,11)( 8,10); poly := sub<Sym(11)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >;
References
- Coxeter, H. S. M.; A Symmetrical Arrangement of Eleven hemi-Icosahedra, Annals of Discrete Mathematics 20 pp103–114 (1984)
- Grünbaum, B.; Regularity of Graphs, Complexes and Designs, in Problèmes Combinatoires et Théorie des Graphes, Colloquium Internationale CNRS, Orsay, 260 pp191–197 (1977)
to this polytope.