Overview
- Group
- SmallGroup(1440,5924)
- Rank
- 5
- Schläfli Type
- {2,10,6,6}
- Vertices, edges, …
- 2, 10, 30, 18, 6
- 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
3-fold
5-fold
9-fold
10-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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76)(79,82)(80,81)(84,87)(85,86)(89,92)(90,91);; s2 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,34)(19,33)(20,37)(21,36)(22,35)(23,44)(24,43)(25,47)(26,46)(27,45)(28,39)(29,38)(30,42)(31,41)(32,40)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,79)(64,78)(65,82)(66,81)(67,80)(68,89)(69,88)(70,92)(71,91)(72,90)(73,84)(74,83)(75,87)(76,86)(77,85);; 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);; s4 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62)(68,73)(69,74)(70,75)(71,76)(72,77)(83,88)(84,89)(85,90)(86,91)(87,92);; 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,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3,
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)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76)(79,82)(80,81)(84,87)(85,86)(89,92)(90,91); s2 := Sym(92)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,34)(19,33)(20,37)(21,36)(22,35)(23,44)(24,43)(25,47)(26,46)(27,45)(28,39)(29,38)(30,42)(31,41)(32,40)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,79)(64,78)(65,82)(66,81)(67,80)(68,89)(69,88)(70,92)(71,91)(72,90)(73,84)(74,83)(75,87)(76,86)(77,85); 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); s4 := Sym(92)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62)(68,73)(69,74)(70,75)(71,76)(72,77)(83,88)(84,89)(85,90)(86,91)(87,92); 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, s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;