Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*864i
if this polytope has a name.
Group : SmallGroup(864,4701)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 36, 108, 18
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,6,2} of size 1728
Vertex Figure Of :
   {2,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,6}*432c
   3-fold quotients : {2,4,6}*288
   6-fold quotients : {2,4,6}*144
   9-fold quotients : {2,12,2}*96
   18-fold quotients : {2,6,2}*48
   27-fold quotients : {2,4,2}*32
   36-fold quotients : {2,3,2}*24
   54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,24,6}*1728h, {4,12,6}*1728q, {2,12,12}*1728k
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(16,17)(18,24)(19,26)
(20,25)(28,29)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(43,44)(45,51)
(46,53)(47,52)(55,56);;
s2 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)(24,28)
(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)(48,49)
(51,55)(52,54)(53,56);;
s3 := ( 3,42)( 4,43)( 5,44)( 6,39)( 7,40)( 8,41)( 9,45)(10,46)(11,47)(12,33)
(13,34)(14,35)(15,30)(16,31)(17,32)(18,36)(19,37)(20,38)(21,51)(22,52)(23,53)
(24,48)(25,49)(26,50)(27,54)(28,55)(29,56);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(56)!(1,2);
s1 := Sym(56)!( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(16,17)(18,24)
(19,26)(20,25)(28,29)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(43,44)
(45,51)(46,53)(47,52)(55,56);
s2 := Sym(56)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)
(24,28)(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)
(48,49)(51,55)(52,54)(53,56);
s3 := Sym(56)!( 3,42)( 4,43)( 5,44)( 6,39)( 7,40)( 8,41)( 9,45)(10,46)(11,47)
(12,33)(13,34)(14,35)(15,30)(16,31)(17,32)(18,36)(19,37)(20,38)(21,51)(22,52)
(23,53)(24,48)(25,49)(26,50)(27,54)(28,55)(29,56);
poly := sub<Sym(56)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

to this polytope