Overview
- Group
- SmallGroup(672,1237)
- Rank
- 4
- Schläfli Type
- {2,42,4}
- Vertices, edges, …
- 2, 42, 84, 4
- Order of s0s1s2s3
- 84
- 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
3-fold
4-fold
6-fold
7-fold
12-fold
14-fold
21-fold
28-fold
42-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,51)(47,50)(48,49)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60)(67,72)(68,71)(69,70)(73,80)(74,86)(75,85)(76,84)(77,83)(78,82)(79,81);; s2 := ( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)(24,32)(25,31)(26,37)(27,36)(28,35)(29,34)(30,33)(38,39)(40,44)(41,43)(45,74)(46,73)(47,79)(48,78)(49,77)(50,76)(51,75)(52,67)(53,66)(54,72)(55,71)(56,70)(57,69)(58,68)(59,81)(60,80)(61,86)(62,85)(63,84)(64,83)(65,82);; s3 := ( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86);; 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*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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*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(86)!(1,2); s1 := Sym(86)!( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,51)(47,50)(48,49)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60)(67,72)(68,71)(69,70)(73,80)(74,86)(75,85)(76,84)(77,83)(78,82)(79,81); s2 := Sym(86)!( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)(24,32)(25,31)(26,37)(27,36)(28,35)(29,34)(30,33)(38,39)(40,44)(41,43)(45,74)(46,73)(47,79)(48,78)(49,77)(50,76)(51,75)(52,67)(53,66)(54,72)(55,71)(56,70)(57,69)(58,68)(59,81)(60,80)(61,86)(62,85)(63,84)(64,83)(65,82); s3 := Sym(86)!( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86); poly := sub<Sym(86)|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*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 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*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 >;