Overview
- Group
- SmallGroup(960,8160)
- Rank
- 5
- Schläfli Type
- {3,2,40,2}
- Vertices, edges, …
- 3, 3, 40, 40, 2
- Order of s0s1s2s3s4
- 120
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 7, 8)( 9,12)(10,14)(11,13)(15,16)(17,22)(18,24)(19,23)(20,26)(21,25)(28,33)(29,32)(30,35)(31,34)(36,37)(38,41)(39,40)(42,43);; s3 := ( 4,10)( 5, 7)( 6,18)( 8,20)( 9,13)(11,15)(12,28)(14,30)(16,21)(17,23)(19,25)(22,36)(24,38)(26,31)(27,32)(29,34)(33,42)(35,39)(37,40)(41,43);; s4 := (44,45);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(45)!(2,3); s1 := Sym(45)!(1,2); s2 := Sym(45)!( 5, 6)( 7, 8)( 9,12)(10,14)(11,13)(15,16)(17,22)(18,24)(19,23)(20,26)(21,25)(28,33)(29,32)(30,35)(31,34)(36,37)(38,41)(39,40)(42,43); s3 := Sym(45)!( 4,10)( 5, 7)( 6,18)( 8,20)( 9,13)(11,15)(12,28)(14,30)(16,21)(17,23)(19,25)(22,36)(24,38)(26,31)(27,32)(29,34)(33,42)(35,39)(37,40)(41,43); s4 := Sym(45)!(44,45); poly := sub<Sym(45)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;