Overview
- Group
- SmallGroup(1440,5921)
- Rank
- 4
- Schläfli Type
- {2,20,6}
- Vertices, edges, …
- 2, 60, 180, 18
- 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
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 := ( 4, 7)( 5, 6)( 8,18)( 9,22)(10,21)(11,20)(12,19)(13,33)(14,37)(15,36)(16,35)(17,34)(24,27)(25,26)(28,38)(29,42)(30,41)(31,40)(32,39)(44,47)(45,46)(49,52)(50,51)(53,63)(54,67)(55,66)(56,65)(57,64)(58,78)(59,82)(60,81)(61,80)(62,79)(69,72)(70,71)(73,83)(74,87)(75,86)(76,85)(77,84)(89,92)(90,91);; s2 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,64)(65,67)(68,74)(69,73)(70,77)(71,76)(72,75)(78,79)(80,82)(83,89)(84,88)(85,92)(86,91)(87,90);; s3 := ( 3,68)( 4,69)( 5,70)( 6,71)( 7,72)( 8,63)( 9,64)(10,65)(11,66)(12,67)(13,73)(14,74)(15,75)(16,76)(17,77)(18,53)(19,54)(20,55)(21,56)(22,57)(23,48)(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62)(33,83)(34,84)(35,85)(36,86)(37,87)(38,78)(39,79)(40,80)(41,81)(42,82)(43,88)(44,89)(45,90)(46,91)(47,92);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(92)!(1,2); s1 := Sym(92)!( 4, 7)( 5, 6)( 8,18)( 9,22)(10,21)(11,20)(12,19)(13,33)(14,37)(15,36)(16,35)(17,34)(24,27)(25,26)(28,38)(29,42)(30,41)(31,40)(32,39)(44,47)(45,46)(49,52)(50,51)(53,63)(54,67)(55,66)(56,65)(57,64)(58,78)(59,82)(60,81)(61,80)(62,79)(69,72)(70,71)(73,83)(74,87)(75,86)(76,85)(77,84)(89,92)(90,91); s2 := Sym(92)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,64)(65,67)(68,74)(69,73)(70,77)(71,76)(72,75)(78,79)(80,82)(83,89)(84,88)(85,92)(86,91)(87,90); s3 := Sym(92)!( 3,68)( 4,69)( 5,70)( 6,71)( 7,72)( 8,63)( 9,64)(10,65)(11,66)(12,67)(13,73)(14,74)(15,75)(16,76)(17,77)(18,53)(19,54)(20,55)(21,56)(22,57)(23,48)(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62)(33,83)(34,84)(35,85)(36,86)(37,87)(38,78)(39,79)(40,80)(41,81)(42,82)(43,88)(44,89)(45,90)(46,91)(47,92); poly := sub<Sym(92)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;