Overview
- Group
- SmallGroup(1344,11709)
- Rank
- 6
- Schläfli Type
- {2,2,14,6,2}
- Vertices, edges, …
- 2, 2, 14, 42, 6, 2
- Order of s0s1s2s3s4s5
- 42
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
7-fold
14-fold
21-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72)(76,81)(77,80)(78,79)(83,88)(84,87)(85,86);; s3 := ( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,62)(13,61)(14,67)(15,66)(16,65)(17,64)(18,63)(19,55)(20,54)(21,60)(22,59)(23,58)(24,57)(25,56)(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,83)(34,82)(35,88)(36,87)(37,86)(38,85)(39,84)(40,76)(41,75)(42,81)(43,80)(44,79)(45,78)(46,77);; s4 := ( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,68)(13,69)(14,70)(15,71)(16,72)(17,73)(18,74)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,88)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67);; s5 := (89,90);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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(90)!(1,2); s1 := Sym(90)!(3,4); s2 := Sym(90)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72)(76,81)(77,80)(78,79)(83,88)(84,87)(85,86); s3 := Sym(90)!( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,62)(13,61)(14,67)(15,66)(16,65)(17,64)(18,63)(19,55)(20,54)(21,60)(22,59)(23,58)(24,57)(25,56)(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,83)(34,82)(35,88)(36,87)(37,86)(38,85)(39,84)(40,76)(41,75)(42,81)(43,80)(44,79)(45,78)(46,77); s4 := Sym(90)!( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,68)(13,69)(14,70)(15,71)(16,72)(17,73)(18,74)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,88)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67); s5 := Sym(90)!(89,90); poly := sub<Sym(90)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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 >;