Polytope of Type {2,2,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,50}*400
if this polytope has a name.
Group : SmallGroup(400,54)
Rank : 4
Schlafli Type : {2,2,50}
Number of vertices, edges, etc : 2, 2, 50, 50
Order of s₀s₁s₂s₃ : 50
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,50,2} of size 800
   {2,2,50,4} of size 1600
Vertex Figure Of :
   {2,2,2,50} of size 800
   {3,2,2,50} of size 1200
   {4,2,2,50} of size 1600
   {5,2,2,50} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,25}*200
   5-fold quotients : {2,2,10}*80
   10-fold quotients : {2,2,5}*40
   25-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,100}*800, {2,4,50}*800, {4,2,50}*800
   3-fold covers : {2,6,50}*1200, {6,2,50}*1200, {2,2,150}*1200
   4-fold covers : {2,4,100}*1600, {4,2,100}*1600, {4,4,50}*1600, {2,2,200}*1600, {2,8,50}*1600, {8,2,50}*1600
   5-fold covers : {2,2,250}*2000, {2,10,50}*2000a, {2,10,50}*2000b, {10,2,50}*2000
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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