Polytope of Type {2,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,50}*200
if this polytope has a name.
Group : SmallGroup(200,13)
Rank : 3
Schlafli Type : {2,50}
Number of vertices, edges, etc : 2, 50, 50
Order of s₀s₁s₂ : 50
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,50,2} of size 400
   {2,50,4} of size 800
   {2,50,6} of size 1200
   {2,50,8} of size 1600
   {2,50,10} of size 2000
   {2,50,10} of size 2000
Vertex Figure Of :
   {2,2,50} of size 400
   {3,2,50} of size 600
   {4,2,50} of size 800
   {5,2,50} of size 1000
   {6,2,50} of size 1200
   {7,2,50} of size 1400
   {8,2,50} of size 1600
   {9,2,50} of size 1800
   {10,2,50} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,25}*100
   5-fold quotients : {2,10}*40
   10-fold quotients : {2,5}*20
   25-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,100}*400, {4,50}*400
   3-fold covers : {6,50}*600, {2,150}*600
   4-fold covers : {4,100}*800, {2,200}*800, {8,50}*800
   5-fold covers : {2,250}*1000, {10,50}*1000a, {10,50}*1000b
   6-fold covers : {12,50}*1200, {6,100}*1200a, {2,300}*1200, {4,150}*1200a
   7-fold covers : {14,50}*1400, {2,350}*1400
   8-fold covers : {4,200}*1600a, {4,100}*1600, {4,200}*1600b, {8,100}*1600a, {8,100}*1600b, {2,400}*1600, {16,50}*1600
   9-fold covers : {18,50}*1800, {2,450}*1800, {6,150}*1800a, {6,150}*1800b, {6,150}*1800c
   10-fold covers : {2,500}*2000, {4,250}*2000, {20,50}*2000a, {10,100}*2000a, {10,100}*2000b, {20,50}*2000b
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope