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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,134272)
Rank : 5
Schlafli Type : {2,2,12,12}
Number of vertices, edges, etc : 2, 2, 12, 72, 12
Order of s₀s₁s₂s₃s₄ : 12
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 : {2,2,6,12}*576b, {2,2,12,6}*576c
   3-fold quotients : {2,2,4,12}*384a
   4-fold quotients : {2,2,6,6}*288b
   6-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a
   8-fold quotients : {2,2,6,3}*144
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {2,2,2,6}*96
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   24-fold quotients : {2,2,2,3}*48
   36-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 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)
(36,39)(37,40)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)(47,62)(48,63)(49,64)
(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)(58,73);;
s3 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)
(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)
(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)
(37,69)(38,74)(39,76)(40,75);;
s4 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)
(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,69)(42,68)(43,70)(44,75)(45,74)
(46,76)(47,72)(48,71)(49,73)(50,60)(51,59)(52,61)(53,66)(54,65)(55,67)(56,63)
(57,62)(58,64);;
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, s4*s2*s3*s2*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, 
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(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)
(35,38)(36,39)(37,40)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)(47,62)(48,63)
(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)(58,73);
s3 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)
(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)
(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)
(36,70)(37,69)(38,74)(39,76)(40,75);
s4 := Sym(76)!( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)
(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,69)(42,68)(43,70)(44,75)
(45,74)(46,76)(47,72)(48,71)(49,73)(50,60)(51,59)(52,61)(53,66)(54,65)(55,67)
(56,63)(57,62)(58,64);
poly := sub<Sym(76)|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, 
s4*s2*s3*s2*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, 
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