Overview
- Group
- SmallGroup(1344,11709)
- Rank
- 6
- Schläfli Type
- {2,2,2,6,14}
- Vertices, edges, …
- 2, 2, 2, 6, 42, 14
- 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 := (5,6);; s3 := ( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,63)(15,64)(16,65)(17,66)(18,67)(19,68)(20,69)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,84)(36,85)(37,86)(38,87)(39,88)(40,89)(41,90)(42,77)(43,78)(44,79)(45,80)(46,81)(47,82)(48,83);; s4 := ( 7,56)( 8,62)( 9,61)(10,60)(11,59)(12,58)(13,57)(14,49)(15,55)(16,54)(17,53)(18,52)(19,51)(20,50)(21,63)(22,69)(23,68)(24,67)(25,66)(26,65)(27,64)(28,77)(29,83)(30,82)(31,81)(32,80)(33,79)(34,78)(35,70)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,84)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85);; s5 := ( 7,29)( 8,28)( 9,34)(10,33)(11,32)(12,31)(13,30)(14,36)(15,35)(16,41)(17,40)(18,39)(19,38)(20,37)(21,43)(22,42)(23,48)(24,47)(25,46)(26,45)(27,44)(49,71)(50,70)(51,76)(52,75)(53,74)(54,73)(55,72)(56,78)(57,77)(58,83)(59,82)(60,81)(61,80)(62,79)(63,85)(64,84)(65,90)(66,89)(67,88)(68,87)(69,86);; 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, s2*s3*s2*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, s3*s4*s5*s4*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(90)!(1,2); s1 := Sym(90)!(3,4); s2 := Sym(90)!(5,6); s3 := Sym(90)!( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,63)(15,64)(16,65)(17,66)(18,67)(19,68)(20,69)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,84)(36,85)(37,86)(38,87)(39,88)(40,89)(41,90)(42,77)(43,78)(44,79)(45,80)(46,81)(47,82)(48,83); s4 := Sym(90)!( 7,56)( 8,62)( 9,61)(10,60)(11,59)(12,58)(13,57)(14,49)(15,55)(16,54)(17,53)(18,52)(19,51)(20,50)(21,63)(22,69)(23,68)(24,67)(25,66)(26,65)(27,64)(28,77)(29,83)(30,82)(31,81)(32,80)(33,79)(34,78)(35,70)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,84)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85); s5 := Sym(90)!( 7,29)( 8,28)( 9,34)(10,33)(11,32)(12,31)(13,30)(14,36)(15,35)(16,41)(17,40)(18,39)(19,38)(20,37)(21,43)(22,42)(23,48)(24,47)(25,46)(26,45)(27,44)(49,71)(50,70)(51,76)(52,75)(53,74)(54,73)(55,72)(56,78)(57,77)(58,83)(59,82)(60,81)(61,80)(62,79)(63,85)(64,84)(65,90)(66,89)(67,88)(68,87)(69,86); 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, s2*s3*s2*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, s3*s4*s5*s4*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;