Polytope of Type {2,48,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48,2}*384
if this polytope has a name.
Group : SmallGroup(384,14577)
Rank : 4
Schlafli Type : {2,48,2}
Number of vertices, edges, etc : 2, 48, 48, 2
Order of s₀s₁s₂s₃ : 48
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,48,2,2} of size 768
   {2,48,2,3} of size 1152
   {2,48,2,5} of size 1920
Vertex Figure Of :
   {2,2,48,2} of size 768
   {3,2,48,2} of size 1152
   {5,2,48,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,24,2}*192
   3-fold quotients : {2,16,2}*128
   4-fold quotients : {2,12,2}*96
   6-fold quotients : {2,8,2}*64
   8-fold quotients : {2,6,2}*48
   12-fold quotients : {2,4,2}*32
   16-fold quotients : {2,3,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,48,4}*768a, {4,48,2}*768a, {2,96,2}*768
   3-fold covers : {2,144,2}*1152, {2,48,6}*1152b, {2,48,6}*1152c, {6,48,2}*1152b, {6,48,2}*1152c
   5-fold covers : {2,240,2}*1920, {2,48,10}*1920, {10,48,2}*1920
Permutation Representation (GAP) :

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

to this polytope