Overview
- Group
- SmallGroup(1344,11527)
- Rank
- 5
- Schläfli Type
- {2,6,4,14}
- Vertices, edges, …
- 2, 6, 12, 28, 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
4-fold
6-fold
7-fold
8-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 := (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)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,79)(52,66)(53,67)(54,68)(55,69)(56,70)(57,71)(58,72)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86);; s3 := ( 3,45)( 4,51)( 5,50)( 6,49)( 7,48)( 8,47)( 9,46)(10,52)(11,58)(12,57)(13,56)(14,55)(15,54)(16,53)(17,59)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)(24,66)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,73)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,80)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81);; 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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!(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)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,79)(52,66)(53,67)(54,68)(55,69)(56,70)(57,71)(58,72)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86); s3 := Sym(86)!( 3,45)( 4,51)( 5,50)( 6,49)( 7,48)( 8,47)( 9,46)(10,52)(11,58)(12,57)(13,56)(14,55)(15,54)(16,53)(17,59)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)(24,66)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,73)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,80)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81); 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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 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 >;