Polytope of Type {48,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,2,2,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,203905)
Rank : 5
Schlafli Type : {48,2,2,5}
Number of vertices, edges, etc : 48, 48, 2, 5, 5
Order of s₀s₁s₂s₃s₄ : 240
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {24,2,2,5}*960
   3-fold quotients : {16,2,2,5}*640
   4-fold quotients : {12,2,2,5}*480
   6-fold quotients : {8,2,2,5}*320
   8-fold quotients : {6,2,2,5}*240
   12-fold quotients : {4,2,2,5}*160
   16-fold quotients : {3,2,2,5}*120
   24-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(18,21)(19,23)
(20,22)(24,27)(25,29)(26,28)(30,33)(31,35)(32,34)(36,39)(37,41)(38,40)(43,46)
(44,45)(47,48);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,25)(17,20)
(18,22)(21,31)(23,26)(24,28)(27,37)(29,32)(30,34)(33,43)(35,38)(36,40)(39,47)
(41,44)(42,45)(46,48);;
s2 := (49,50);;
s3 := (52,53)(54,55);;
s4 := (51,52)(53,54);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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*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*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*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(55)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(18,21)
(19,23)(20,22)(24,27)(25,29)(26,28)(30,33)(31,35)(32,34)(36,39)(37,41)(38,40)
(43,46)(44,45)(47,48);
s1 := Sym(55)!( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,25)
(17,20)(18,22)(21,31)(23,26)(24,28)(27,37)(29,32)(30,34)(33,43)(35,38)(36,40)
(39,47)(41,44)(42,45)(46,48);
s2 := Sym(55)!(49,50);
s3 := Sym(55)!(52,53)(54,55);
s4 := Sym(55)!(51,52)(53,54);
poly := sub<Sym(55)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope