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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,12,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,153178)
Rank : 6
Schlafli Type : {2,2,2,12,6}
Number of vertices, edges, etc : 2, 2, 2, 12, 36, 6
Order of s₀s₁s₂s₃s₄s₅ : 12
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 : {2,2,2,6,6}*576a
   3-fold quotients : {2,2,2,12,2}*384, {2,2,2,4,6}*384a
   6-fold quotients : {2,2,2,2,6}*192, {2,2,2,6,2}*192
   9-fold quotients : {2,2,2,4,2}*128
   12-fold quotients : {2,2,2,2,3}*96, {2,2,2,3,2}*96
   18-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,43)( 8,44)( 9,45)(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)
(17,53)(18,54)(19,58)(20,59)(21,60)(22,55)(23,56)(24,57)(25,70)(26,71)(27,72)
(28,76)(29,77)(30,78)(31,73)(32,74)(33,75)(34,61)(35,62)(36,63)(37,67)(38,68)
(39,69)(40,64)(41,65)(42,66);;
s4 := ( 7,64)( 8,66)( 9,65)(10,61)(11,63)(12,62)(13,67)(14,69)(15,68)(16,73)
(17,75)(18,74)(19,70)(20,72)(21,71)(22,76)(23,78)(24,77)(25,46)(26,48)(27,47)
(28,43)(29,45)(30,44)(31,49)(32,51)(33,50)(34,55)(35,57)(36,56)(37,52)(38,54)
(39,53)(40,58)(41,60)(42,59);;
s5 := ( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)
(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)
(70,71)(73,74)(76,77);;
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, s2*s3*s2*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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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(78)!(1,2);
s1 := Sym(78)!(3,4);
s2 := Sym(78)!(5,6);
s3 := Sym(78)!( 7,43)( 8,44)( 9,45)(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)
(16,52)(17,53)(18,54)(19,58)(20,59)(21,60)(22,55)(23,56)(24,57)(25,70)(26,71)
(27,72)(28,76)(29,77)(30,78)(31,73)(32,74)(33,75)(34,61)(35,62)(36,63)(37,67)
(38,68)(39,69)(40,64)(41,65)(42,66);
s4 := Sym(78)!( 7,64)( 8,66)( 9,65)(10,61)(11,63)(12,62)(13,67)(14,69)(15,68)
(16,73)(17,75)(18,74)(19,70)(20,72)(21,71)(22,76)(23,78)(24,77)(25,46)(26,48)
(27,47)(28,43)(29,45)(30,44)(31,49)(32,51)(33,50)(34,55)(35,57)(36,56)(37,52)
(38,54)(39,53)(40,58)(41,60)(42,59);
s5 := Sym(78)!( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74)(76,77);
poly := sub<Sym(78)|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, 
s2*s3*s2*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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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