Polytope of Type {3,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,155790)
Rank : 4
Schlafli Type : {3,6,4}
Number of vertices, edges, etc : 12, 72, 96, 8
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   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) :
   3-fold quotients : {3,6,4}*384b
   4-fold quotients : {3,6,2}*288
   6-fold quotients : {3,3,4}*192
   12-fold quotients : {3,6,2}*96
   16-fold quotients : {3,6,2}*72
   24-fold quotients : {3,3,2}*48
   48-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope