Overview
- Group
- SmallGroup(1440,5890)
- Rank
- 4
- Schläfli Type
- {2,4,30}
- Vertices, edges, …
- 2, 12, 180, 90
- Order of s0s1s2s3
- 20
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
5-fold
9-fold
10-fold
18-fold
36-fold
45-fold
90-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,28)(14,29)(15,30)(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37);; s2 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(18,43)(19,47)(20,46)(21,45)(22,44)(23,33)(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39);; s3 := ( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,19)( 9,18)(10,22)(11,21)(12,20)(13,29)(14,28)(15,32)(16,31)(17,30)(33,39)(34,38)(35,42)(36,41)(37,40)(43,44)(45,47);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(1,2); s1 := Sym(47)!( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,28)(14,29)(15,30)(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37); s2 := Sym(47)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(18,43)(19,47)(20,46)(21,45)(22,44)(23,33)(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39); s3 := Sym(47)!( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,19)( 9,18)(10,22)(11,21)(12,20)(13,29)(14,28)(15,32)(16,31)(17,30)(33,39)(34,38)(35,42)(36,41)(37,40)(43,44)(45,47); poly := sub<Sym(47)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2 >;