Overview
- Group
- SmallGroup(1600,8167)
- Rank
- 5
- Schläfli Type
- {5,2,8,10}
- Vertices, edges, …
- 5, 5, 8, 40, 10
- Order of s0s1s2s3s4
- 40
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5);; s1 := (1,2)(3,4);; s2 := (16,21)(17,22)(18,23)(19,24)(20,25)(26,41)(27,42)(28,43)(29,44)(30,45)(31,36)(32,37)(33,38)(34,39)(35,40);; s3 := ( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,31)(12,35)(13,34)(14,33)(15,32)(16,41)(17,45)(18,44)(19,43)(20,42)(21,36)(22,40)(23,39)(24,38)(25,37);; s4 := ( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45);; 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,
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(45)!(2,3)(4,5); s1 := Sym(45)!(1,2)(3,4); s2 := Sym(45)!(16,21)(17,22)(18,23)(19,24)(20,25)(26,41)(27,42)(28,43)(29,44)(30,45)(31,36)(32,37)(33,38)(34,39)(35,40); s3 := Sym(45)!( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,31)(12,35)(13,34)(14,33)(15,32)(16,41)(17,45)(18,44)(19,43)(20,42)(21,36)(22,40)(23,39)(24,38)(25,37); s4 := Sym(45)!( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45); 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, s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;