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