Polytope of Type {4,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,12}*576f
if this polytope has a name.
Group : SmallGroup(576,8660)
Rank : 4
Schlafli Type : {4,6,12}
Number of vertices, edges, etc : 4, 12, 36, 12
Order of s₀s₁s₂s₃ : 3
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,12,2} of size 1152
Vertex Figure Of :
   {2,4,6,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,6,4}*192e
   6-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,12}*1152e, {4,6,12}*1152g
   3-fold covers : {4,6,36}*1728d, {4,18,12}*1728e, {4,6,12}*1728i
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope