Overview
- Group
- SmallGroup(1920,240988)
- Rank
- 4
- Schläfli Type
- {2,20,6}
- Vertices, edges, …
- 2, 80, 240, 24
- 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
2-fold
4-fold
8-fold
16-fold
120-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4,47)( 5,43)( 6,19)( 7,21)( 9,32)(10,50)(11,38)(12,49)(13,25)(14,36)(15,24)(16,42)(17,41)(22,28)(23,31)(26,40)(27,39)(29,48)(30,33)(37,44);; s2 := ( 3, 6)( 4,15)( 5,10)( 7,18)( 8,19)( 9,45)(11,32)(12,37)(13,29)(14,24)(16,26)(17,27)(20,21)(22,48)(23,30)(25,35)(28,31)(33,42)(34,41)(36,44)(38,40)(39,49)(43,46)(47,50);; s3 := ( 3,34)( 4,48)( 5,15)( 6,14)( 7,33)( 8,46)( 9,42)(10,40)(11,49)(12,38)(13,31)(16,32)(17,37)(18,35)(19,36)(20,45)(21,30)(22,27)(23,25)(24,43)(26,50)(28,39)(29,47)(41,44)(51,52);; 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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(52)!(1,2); s1 := Sym(52)!( 4,47)( 5,43)( 6,19)( 7,21)( 9,32)(10,50)(11,38)(12,49)(13,25)(14,36)(15,24)(16,42)(17,41)(22,28)(23,31)(26,40)(27,39)(29,48)(30,33)(37,44); s2 := Sym(52)!( 3, 6)( 4,15)( 5,10)( 7,18)( 8,19)( 9,45)(11,32)(12,37)(13,29)(14,24)(16,26)(17,27)(20,21)(22,48)(23,30)(25,35)(28,31)(33,42)(34,41)(36,44)(38,40)(39,49)(43,46)(47,50); s3 := Sym(52)!( 3,34)( 4,48)( 5,15)( 6,14)( 7,33)( 8,46)( 9,42)(10,40)(11,49)(12,38)(13,31)(16,32)(17,37)(18,35)(19,36)(20,45)(21,30)(22,27)(23,25)(24,43)(26,50)(28,39)(29,47)(41,44)(51,52); poly := sub<Sym(52)|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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 >;