Overview
- Group
- SmallGroup(1440,1593)
- Rank
- 5
- Schläfli Type
- {5,2,4,18}
- Vertices, edges, …
- 5, 5, 4, 36, 18
- Order of s0s1s2s3s4
- 180
- 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
3-fold
4-fold
6-fold
9-fold
12-fold
18-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 := (24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(32,41);; s3 := ( 6,24)( 7,26)( 8,25)( 9,31)(10,30)(11,32)(12,28)(13,27)(14,29)(15,33)(16,35)(17,34)(18,40)(19,39)(20,41)(21,37)(22,36)(23,38);; s4 := ( 6, 9)( 7,11)( 8,10)(12,13)(15,18)(16,20)(17,19)(21,22)(24,27)(25,29)(26,28)(30,31)(33,36)(34,38)(35,37)(39,40);; 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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(41)!(2,3)(4,5); s1 := Sym(41)!(1,2)(3,4); s2 := Sym(41)!(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(32,41); s3 := Sym(41)!( 6,24)( 7,26)( 8,25)( 9,31)(10,30)(11,32)(12,28)(13,27)(14,29)(15,33)(16,35)(17,34)(18,40)(19,39)(20,41)(21,37)(22,36)(23,38); s4 := Sym(41)!( 6, 9)( 7,11)( 8,10)(12,13)(15,18)(16,20)(17,19)(21,22)(24,27)(25,29)(26,28)(30,31)(33,36)(34,38)(35,37)(39,40); poly := sub<Sym(41)|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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;