Polytope of Type {2,2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 5
Schlafli Type : {2,2,6,12}
Number of vertices, edges, etc : 2, 2, 12, 72, 24
Order of s₀s₁s₂s₃s₄ : 6
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 : {2,2,3,12}*576
   3-fold quotients : {2,2,6,4}*384
   4-fold quotients : {2,2,6,6}*288c
   6-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
   8-fold quotients : {2,2,3,6}*144
   12-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
   24-fold quotients : {2,2,3,2}*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 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,29)(18,31)(19,30)(20,32)(21,37)
(22,39)(23,38)(24,40)(25,33)(26,35)(27,34)(28,36)(42,43)(45,49)(46,51)(47,50)
(48,52)(53,65)(54,67)(55,66)(56,68)(57,73)(58,75)(59,74)(60,76)(61,69)(62,71)
(63,70)(64,72);;
s3 := ( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)(10,54)(11,56)(12,55)(13,61)(14,62)
(15,64)(16,63)(17,45)(18,46)(19,48)(20,47)(21,41)(22,42)(23,44)(24,43)(25,49)
(26,50)(27,52)(28,51)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)(36,67)
(37,73)(38,74)(39,76)(40,75);;
s4 := ( 5, 8)( 6, 7)( 9,16)(10,15)(11,14)(12,13)(17,20)(18,19)(21,28)(22,27)
(23,26)(24,25)(29,32)(30,31)(33,40)(34,39)(35,38)(36,37)(41,44)(42,43)(45,52)
(46,51)(47,50)(48,49)(53,56)(54,55)(57,64)(58,63)(59,62)(60,61)(65,68)(66,67)
(69,76)(70,75)(71,74)(72,73);;
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope