Polytope of Type {12,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,4}*768b
if this polytope has a name.
Group : SmallGroup(768,201151)
Rank : 4
Schlafli Type : {12,4,4}
Number of vertices, edges, etc : 24, 48, 16, 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 : {12,4,4}*384, {12,4,2}*384a
   3-fold quotients : {4,4,4}*256b
   4-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
   6-fold quotients : {4,4,4}*128, {4,4,2}*128
   8-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
   12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   16-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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