Polytope of Type {50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50}*100
Also Known As : 50-gon, {50}. if this polytope has another name.
Group : SmallGroup(100,4)
Rank : 2
Schlafli Type : {50}
Number of vertices, edges, etc : 50, 50
Order of s₀s₁ : 50
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {50,2} of size 200
   {50,4} of size 400
   {50,6} of size 600
   {50,8} of size 800
   {50,10} of size 1000
   {50,10} of size 1000
   {50,12} of size 1200
   {50,14} of size 1400
   {50,16} of size 1600
   {50,4} of size 1600
   {50,4} of size 1600
   {50,18} of size 1800
   {50,20} of size 2000
   {50,20} of size 2000
Vertex Figure Of :
   {2,50} of size 200
   {4,50} of size 400
   {6,50} of size 600
   {8,50} of size 800
   {10,50} of size 1000
   {10,50} of size 1000
   {12,50} of size 1200
   {14,50} of size 1400
   {16,50} of size 1600
   {4,50} of size 1600
   {4,50} of size 1600
   {18,50} of size 1800
   {20,50} of size 2000
   {20,50} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {25}*50
   5-fold quotients : {10}*20
   10-fold quotients : {5}*10
   25-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {100}*200
   3-fold covers : {150}*300
   4-fold covers : {200}*400
   5-fold covers : {250}*500
   6-fold covers : {300}*600
   7-fold covers : {350}*700
   8-fold covers : {400}*800
   9-fold covers : {450}*900
   10-fold covers : {500}*1000
   11-fold covers : {550}*1100
   12-fold covers : {600}*1200
   13-fold covers : {650}*1300
   14-fold covers : {700}*1400
   15-fold covers : {750}*1500
   16-fold covers : {800}*1600
   17-fold covers : {850}*1700
   18-fold covers : {900}*1800
   19-fold covers : {950}*1900
   20-fold covers : {1000}*2000
Permutation Representation (GAP) :

s0 := ( 3, 4)( 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);;
s1 := ( 1, 5)( 2, 3)( 4, 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)(48,50);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(50)!( 3, 4)( 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);
s1 := Sym(50)!( 1, 5)( 2, 3)( 4, 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)(48,50);
poly := sub<Sym(50)|s0,s1>;

Finitely Presented Group Representation (Magma) :

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

References : None.
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