Polytope of Type {2,2,4,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,3,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 6
Schlafli Type : {2,2,4,3,6}
Number of vertices, edges, etc : 2, 2, 8, 12, 18, 6
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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 : {2,2,4,3,6}*576
   3-fold quotients : {2,2,4,3,2}*384
   4-fold quotients : {2,2,2,3,6}*288
   6-fold quotients : {2,2,4,3,2}*192
   12-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)(13,50)(14,49)
(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)(24,59)(25,62)
(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)(35,72)(36,71)
(37,74)(38,73)(39,76)(40,75);;
s3 := ( 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);;
s4 := ( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(13,25)(14,26)
(15,28)(16,27)(29,33)(30,34)(31,36)(32,35)(39,40)(41,57)(42,58)(43,60)(44,59)
(45,53)(46,54)(47,56)(48,55)(49,61)(50,62)(51,64)(52,63)(65,69)(66,70)(67,72)
(68,71)(75,76);;
s5 := ( 9,13)(10,14)(11,15)(12,16)(21,25)(22,26)(23,27)(24,28)(33,37)(34,38)
(35,39)(36,40)(45,49)(46,50)(47,51)(48,52)(57,61)(58,62)(59,63)(60,64)(69,73)
(70,74)(71,75)(72,76);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)(13,50)
(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)(24,59)
(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)(35,72)
(36,71)(37,74)(38,73)(39,76)(40,75);
s3 := 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);
s4 := Sym(76)!( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(13,25)
(14,26)(15,28)(16,27)(29,33)(30,34)(31,36)(32,35)(39,40)(41,57)(42,58)(43,60)
(44,59)(45,53)(46,54)(47,56)(48,55)(49,61)(50,62)(51,64)(52,63)(65,69)(66,70)
(67,72)(68,71)(75,76);
s5 := Sym(76)!( 9,13)(10,14)(11,15)(12,16)(21,25)(22,26)(23,27)(24,28)(33,37)
(34,38)(35,39)(36,40)(45,49)(46,50)(47,51)(48,52)(57,61)(58,62)(59,63)(60,64)
(69,73)(70,74)(71,75)(72,76);
poly := sub<Sym(76)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 >;

to this polytope