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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,14}*1344
if this polytope has a name.
Group : SmallGroup(1344,11516)
Rank : 5
Schlafli Type : {2,2,12,14}
Number of vertices, edges, etc : 2, 2, 12, 84, 14
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 : {2,2,6,14}*672
   3-fold quotients : {2,2,4,14}*448
   6-fold quotients : {2,2,2,14}*224
   7-fold quotients : {2,2,12,2}*192
   12-fold quotients : {2,2,2,7}*112
   14-fold quotients : {2,2,6,2}*96
   21-fold quotients : {2,2,4,2}*64
   28-fold quotients : {2,2,3,2}*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 := (12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(18,25)(33,40)(34,41)(35,42)
(36,43)(37,44)(38,45)(39,46)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)
(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,75)(62,76)(63,77)(64,78)
(65,79)(66,80)(67,81);;
s3 := ( 5,54)( 6,60)( 7,59)( 8,58)( 9,57)(10,56)(11,55)(12,47)(13,53)(14,52)
(15,51)(16,50)(17,49)(18,48)(19,61)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)
(26,75)(27,81)(28,80)(29,79)(30,78)(31,77)(32,76)(33,68)(34,74)(35,73)(36,72)
(37,71)(38,70)(39,69)(40,82)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83);;
s4 := ( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)(26,27)
(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)(50,52)
(54,55)(56,60)(57,59)(61,62)(63,67)(64,66)(68,69)(70,74)(71,73)(75,76)(77,81)
(78,80)(82,83)(84,88)(85,87);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope