Overview
- Group
- SmallGroup(1344,11709)
- Rank
- 6
- Schläfli Type
- {2,14,6,2,2}
- Vertices, edges, …
- 2, 14, 42, 6, 2, 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 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)(53,58)(54,57)(55,56)(60,65)(61,64)(62,63)(67,72)(68,71)(69,70)(74,79)(75,78)(76,77)(81,86)(82,85)(83,84);; s2 := ( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,60)(11,59)(12,65)(13,64)(14,63)(15,62)(16,61)(17,53)(18,52)(19,58)(20,57)(21,56)(22,55)(23,54)(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,81)(32,80)(33,86)(34,85)(35,84)(36,83)(37,82)(38,74)(39,73)(40,79)(41,78)(42,77)(43,76)(44,75);; s3 := ( 3,73)( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,66)(11,67)(12,68)(13,69)(14,70)(15,71)(16,72)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);; s4 := (87,88);; 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, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*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*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(90)!(1,2); s1 := Sym(90)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)(53,58)(54,57)(55,56)(60,65)(61,64)(62,63)(67,72)(68,71)(69,70)(74,79)(75,78)(76,77)(81,86)(82,85)(83,84); s2 := Sym(90)!( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,60)(11,59)(12,65)(13,64)(14,63)(15,62)(16,61)(17,53)(18,52)(19,58)(20,57)(21,56)(22,55)(23,54)(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,81)(32,80)(33,86)(34,85)(35,84)(36,83)(37,82)(38,74)(39,73)(40,79)(41,78)(42,77)(43,76)(44,75); s3 := Sym(90)!( 3,73)( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,66)(11,67)(12,68)(13,69)(14,70)(15,71)(16,72)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65); s4 := Sym(90)!(87,88); 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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*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*s1*s2 >;