Polytope of Type {4,2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,48}*768
if this polytope has a name.
Group : SmallGroup(768,326223)
Rank : 4
Schlafli Type : {4,2,48}
Number of vertices, edges, etc : 4, 4, 48, 48
Order of s₀s₁s₂s₃ : 48
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {4,2,24}*384, {2,2,48}*384
   3-fold quotients : {4,2,16}*256
   4-fold quotients : {4,2,12}*192, {2,2,24}*192
   6-fold quotients : {4,2,8}*128, {2,2,16}*128
   8-fold quotients : {2,2,12}*96, {4,2,6}*96
   12-fold quotients : {4,2,4}*64, {2,2,8}*64
   16-fold quotients : {4,2,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {4,2,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(22,25)(23,27)
(24,26)(28,31)(29,33)(30,32)(34,37)(35,39)(36,38)(40,43)(41,45)(42,44)(47,50)
(48,49)(51,52);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,12)(10,14)(13,23)(15,18)(16,20)(19,29)(21,24)
(22,26)(25,35)(27,30)(28,32)(31,41)(33,36)(34,38)(37,47)(39,42)(40,44)(43,51)
(45,48)(46,49)(50,52);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!(2,3);
s1 := Sym(52)!(1,2)(3,4);
s2 := Sym(52)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(22,25)
(23,27)(24,26)(28,31)(29,33)(30,32)(34,37)(35,39)(36,38)(40,43)(41,45)(42,44)
(47,50)(48,49)(51,52);
s3 := Sym(52)!( 5,11)( 6, 8)( 7,17)( 9,12)(10,14)(13,23)(15,18)(16,20)(19,29)
(21,24)(22,26)(25,35)(27,30)(28,32)(31,41)(33,36)(34,38)(37,47)(39,42)(40,44)
(43,51)(45,48)(46,49)(50,52);
poly := sub<Sym(52)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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