Polytope of Type {4,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*768b
if this polytope has a name.
Group : SmallGroup(768,201150)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 8, 48, 48, 4
Order of s₀s₁s₂s₃ : 12
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) :
   2-fold quotients : {4,12,4}*384a, {4,12,2}*384a
   3-fold quotients : {4,4,4}*256b
   4-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
   6-fold quotients : {4,4,4}*128, {4,4,2}*128
   8-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,6,2}*96a
   12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   16-fold quotients : {2,6,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {2,3,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
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