Overview
- Group
- SmallGroup(672,1140)
- Rank
- 4
- Schläfli Type
- {2,12,14}
- Vertices, edges, …
- 2, 12, 84, 14
- 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)(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,80)(53,81)(54,82)(55,83)(56,84)(57,85)(58,86)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79);; s2 := ( 3,52)( 4,58)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,45)(11,51)(12,50)(13,49)(14,48)(15,47)(16,46)(17,59)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)(24,73)(25,79)(26,78)(27,77)(28,76)(29,75)(30,74)(31,66)(32,72)(33,71)(34,70)(35,69)(36,68)(37,67)(38,80)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81);; s3 := ( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)(24,25)(26,30)(27,29)(31,32)(33,37)(34,36)(38,39)(40,44)(41,43)(45,46)(47,51)(48,50)(52,53)(54,58)(55,57)(59,60)(61,65)(62,64)(66,67)(68,72)(69,71)(73,74)(75,79)(76,78)(80,81)(82,86)(83,85);; 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*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 ];;
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)(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,80)(53,81)(54,82)(55,83)(56,84)(57,85)(58,86)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79); s2 := Sym(86)!( 3,52)( 4,58)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,45)(11,51)(12,50)(13,49)(14,48)(15,47)(16,46)(17,59)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)(24,73)(25,79)(26,78)(27,77)(28,76)(29,75)(30,74)(31,66)(32,72)(33,71)(34,70)(35,69)(36,68)(37,67)(38,80)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81); s3 := Sym(86)!( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)(24,25)(26,30)(27,29)(31,32)(33,37)(34,36)(38,39)(40,44)(41,43)(45,46)(47,51)(48,50)(52,53)(54,58)(55,57)(59,60)(61,65)(62,64)(66,67)(68,72)(69,71)(73,74)(75,79)(76,78)(80,81)(82,86)(83,85); 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*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 >;