Polytope of Type {2,2,14,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,12}*1344
if this polytope has a name.
Group : SmallGroup(1344,11516)
Rank : 5
Schlafli Type : {2,2,14,12}
Number of vertices, edges, etc : 2, 2, 14, 84, 12
Order of s₀s₁s₂s₃s₄ : 84
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,14,6}*672
   3-fold quotients : {2,2,14,4}*448
   6-fold quotients : {2,2,14,2}*224
   7-fold quotients : {2,2,2,12}*192
   12-fold quotients : {2,2,7,2}*112
   14-fold quotients : {2,2,2,6}*96
   21-fold quotients : {2,2,2,4}*64
   28-fold quotients : {2,2,2,3}*48
   42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 6)( 7,11)( 8,10)(12,20)(13,19)(14,25)(15,24)(16,23)(17,22)(18,21)
(26,27)(28,32)(29,31)(33,41)(34,40)(35,46)(36,45)(37,44)(38,43)(39,42)(47,69)
(48,68)(49,74)(50,73)(51,72)(52,71)(53,70)(54,83)(55,82)(56,88)(57,87)(58,86)
(59,85)(60,84)(61,76)(62,75)(63,81)(64,80)(65,79)(66,78)(67,77);;
s4 := ( 5,54)( 6,55)( 7,56)( 8,57)( 9,58)(10,59)(11,60)(12,47)(13,48)(14,49)
(15,50)(16,51)(17,52)(18,53)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)
(26,75)(27,76)(28,77)(29,78)(30,79)(31,80)(32,81)(33,68)(34,69)(35,70)(36,71)
(37,72)(38,73)(39,74)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*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, 
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(88)!(1,2);
s1 := Sym(88)!(3,4);
s2 := Sym(88)!( 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(88)!( 5, 6)( 7,11)( 8,10)(12,20)(13,19)(14,25)(15,24)(16,23)(17,22)
(18,21)(26,27)(28,32)(29,31)(33,41)(34,40)(35,46)(36,45)(37,44)(38,43)(39,42)
(47,69)(48,68)(49,74)(50,73)(51,72)(52,71)(53,70)(54,83)(55,82)(56,88)(57,87)
(58,86)(59,85)(60,84)(61,76)(62,75)(63,81)(64,80)(65,79)(66,78)(67,77);
s4 := Sym(88)!( 5,54)( 6,55)( 7,56)( 8,57)( 9,58)(10,59)(11,60)(12,47)(13,48)
(14,49)(15,50)(16,51)(17,52)(18,53)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)
(25,67)(26,75)(27,76)(28,77)(29,78)(30,79)(31,80)(32,81)(33,68)(34,69)(35,70)
(36,71)(37,72)(38,73)(39,74)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88);
poly := sub<Sym(88)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*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, 
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 >;

to this polytope