Polytope of Type {2,12,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,5}*960
if this polytope has a name.
Group : SmallGroup(960,10889)
Rank : 4
Schlafli Type : {2,12,5}
Number of vertices, edges, etc : 2, 48, 120, 20
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,5,2} of size 1920
Vertex Figure Of :
   {2,2,12,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,5}*480b
   4-fold quotients : {2,3,5}*240, {2,6,5}*240b, {2,6,5}*240c
   8-fold quotients : {2,3,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,5}*1920, {2,12,10}*1920e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope