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}*576b
if this polytope has a name.
Group : SmallGroup(576,8545)
Rank : 5
Schlafli Type : {2,2,12,6}
Number of vertices, edges, etc : 2, 2, 12, 36, 6
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,12,6,2} of size 1152
   {2,2,12,6,3} of size 1728
Vertex Figure Of :
   {2,2,2,12,6} of size 1152
   {3,2,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,6,6}*288c
   3-fold quotients : {2,2,12,2}*192
   4-fold quotients : {2,2,3,6}*144
   6-fold quotients : {2,2,6,2}*96
   9-fold quotients : {2,2,4,2}*64
   12-fold quotients : {2,2,3,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12,6}*1152b, {2,2,12,12}*1152c, {4,2,12,6}*1152c, {2,2,24,6}*1152c
   3-fold covers : {2,2,36,6}*1728b, {2,2,12,6}*1728a, {2,6,12,6}*1728d, {2,6,12,6}*1728e, {6,2,12,6}*1728b, {2,2,12,6}*1728g
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope