Overview
- Group
- SmallGroup(1344,11527)
- Rank
- 5
- Schläfli Type
- {2,4,6,14}
- Vertices, edges, …
- 2, 4, 12, 42, 14
- Order of s0s1s2s3s4
- 84
- Order of s0s1s2s3s4s3s2s1
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86);; s2 := ( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,59)(11,60)(12,61)(13,62)(14,63)(15,64)(16,65)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,80)(32,81)(33,82)(34,83)(35,84)(36,85)(37,86)(38,73)(39,74)(40,75)(41,76)(42,77)(43,78)(44,79);; s3 := ( 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)(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63)(66,73)(67,79)(68,78)(69,77)(70,76)(71,75)(72,74)(81,86)(82,85)(83,84);; s4 := ( 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,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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(86)!(1,2); s1 := Sym(86)!(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86); s2 := Sym(86)!( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,59)(11,60)(12,61)(13,62)(14,63)(15,64)(16,65)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,80)(32,81)(33,82)(34,83)(35,84)(36,85)(37,86)(38,73)(39,74)(40,75)(41,76)(42,77)(43,78)(44,79); s3 := 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)(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63)(66,73)(67,79)(68,78)(69,77)(70,76)(71,75)(72,74)(81,86)(82,85)(83,84); s4 := 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,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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;