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

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

Permutation Representation (Magma) :

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

to this polytope