Polytope of Type {4,24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,4}*768b
if this polytope has a name.
Group : SmallGroup(768,201204)
Rank : 4
Schlafli Type : {4,24,4}
Number of vertices, edges, etc : 4, 48, 48, 4
Order of s₀s₁s₂s₃ : 24
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, {2,24,4}*384b
   3-fold quotients : {4,8,4}*256b
   4-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
   6-fold quotients : {4,4,4}*128, {2,8,4}*128b
   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 := (25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)(40,46)
(41,47)(42,48);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)
(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)(21,47)
(22,43)(23,45)(24,44);;
s2 := ( 1, 3)( 4, 6)( 7, 9)(10,12)(13,18)(14,17)(15,16)(19,24)(20,23)(21,22)
(25,39)(26,38)(27,37)(28,42)(29,41)(30,40)(31,45)(32,44)(33,43)(34,48)(35,47)
(36,46);;
s3 := (13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(37,40)(38,41)(39,42)(43,46)
(44,47)(45,48);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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