Polytope of Type {8,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,3,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,155791)
Rank : 4
Schlafli Type : {8,3,6}
Number of vertices, edges, etc : 32, 48, 36, 6
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {8,3,2}*384
   4-fold quotients : {4,3,6}*288
   8-fold quotients : {4,3,6}*144
   12-fold quotients : {4,3,2}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {4,3,2}*48
   48-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope