Overview
- Group
- SmallGroup(672,1141)
- Rank
- 4
- Schläfli Type
- {2,28,6}
- Vertices, edges, …
- 2, 28, 84, 6
- 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
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)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(45,66)(46,72)(47,71)(48,70)(49,69)(50,68)(51,67)(52,73)(53,79)(54,78)(55,77)(56,76)(57,75)(58,74)(59,80)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81);; s2 := ( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,60)(11,59)(12,65)(13,64)(14,63)(15,62)(16,61)(17,53)(18,52)(19,58)(20,57)(21,56)(22,55)(23,54)(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,81)(32,80)(33,86)(34,85)(35,84)(36,83)(37,82)(38,74)(39,73)(40,79)(41,78)(42,77)(43,76)(44,75);; s3 := ( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(45,52)(46,53)(47,54)(48,55)(49,56)(50,57)(51,58)(66,73)(67,74)(68,75)(69,76)(70,77)(71,78)(72,79);; 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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(86)!(1,2); s1 := Sym(86)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(45,66)(46,72)(47,71)(48,70)(49,69)(50,68)(51,67)(52,73)(53,79)(54,78)(55,77)(56,76)(57,75)(58,74)(59,80)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81); s2 := Sym(86)!( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,60)(11,59)(12,65)(13,64)(14,63)(15,62)(16,61)(17,53)(18,52)(19,58)(20,57)(21,56)(22,55)(23,54)(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,81)(32,80)(33,86)(34,85)(35,84)(36,83)(37,82)(38,74)(39,73)(40,79)(41,78)(42,77)(43,76)(44,75); s3 := Sym(86)!( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(45,52)(46,53)(47,54)(48,55)(49,56)(50,57)(51,58)(66,73)(67,74)(68,75)(69,76)(70,77)(71,78)(72,79); 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*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 >;