Overview
- Group
- SmallGroup(1440,5924)
- Rank
- 5
- Schläfli Type
- {2,6,6,10}
- Vertices, edges, …
- 2, 6, 18, 30, 10
- Order of s0s1s2s3s4
- 30
- 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
5-fold
6-fold
9-fold
10-fold
12-fold
15-fold
18-fold
30-fold
45-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(18,33)(19,34)(20,35)(21,36)(22,37)(23,43)(24,44)(25,45)(26,46)(27,47)(28,38)(29,39)(30,40)(31,41)(32,42)(53,58)(54,59)(55,60)(56,61)(57,62)(63,78)(64,79)(65,80)(66,81)(67,82)(68,88)(69,89)(70,90)(71,91)(72,92)(73,83)(74,84)(75,85)(76,86)(77,87);; s2 := ( 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);; s3 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59)(64,67)(65,66)(68,73)(69,77)(70,76)(71,75)(72,74)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)(87,89);; s4 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)(80,82)(83,84)(85,87)(88,89)(90,92);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
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(92)!(1,2); s1 := Sym(92)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(18,33)(19,34)(20,35)(21,36)(22,37)(23,43)(24,44)(25,45)(26,46)(27,47)(28,38)(29,39)(30,40)(31,41)(32,42)(53,58)(54,59)(55,60)(56,61)(57,62)(63,78)(64,79)(65,80)(66,81)(67,82)(68,88)(69,89)(70,90)(71,91)(72,92)(73,83)(74,84)(75,85)(76,86)(77,87); s2 := 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); s3 := Sym(92)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59)(64,67)(65,66)(68,73)(69,77)(70,76)(71,75)(72,74)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)(87,89); s4 := Sym(92)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)(80,82)(83,84)(85,87)(88,89)(90,92); poly := sub<Sym(92)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;