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