Polytope of Type {25}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25}*50
Also Known As : 25-gon, {25}. if this polytope has another name.
Group : SmallGroup(50,1)
Rank : 2
Schlafli Type : {25}
Number of vertices, edges, etc : 25, 25
Order of s₀s₁ : 25
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {25,2} of size 100
   {25,10} of size 500
   {25,4} of size 800
   {25,8} of size 1600
   {25,8} of size 1600
   {25,4} of size 1600
Vertex Figure Of :
   {2,25} of size 100
   {10,25} of size 500
   {4,25} of size 800
   {8,25} of size 1600
   {8,25} of size 1600
   {4,25} of size 1600
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5}*10
Covers (Minimal Covers in Boldface) :
   2-fold covers : {50}*100
   3-fold covers : {75}*150
   4-fold covers : {100}*200
   5-fold covers : {125}*250
   6-fold covers : {150}*300
   7-fold covers : {175}*350
   8-fold covers : {200}*400
   9-fold covers : {225}*450
   10-fold covers : {250}*500
   11-fold covers : {275}*550
   12-fold covers : {300}*600
   13-fold covers : {325}*650
   14-fold covers : {350}*700
   15-fold covers : {375}*750
   16-fold covers : {400}*800
   17-fold covers : {425}*850
   18-fold covers : {450}*900
   19-fold covers : {475}*950
   20-fold covers : {500}*1000
   21-fold covers : {525}*1050
   22-fold covers : {550}*1100
   23-fold covers : {575}*1150
   24-fold covers : {600}*1200
   25-fold covers : {625}*1250
   26-fold covers : {650}*1300
   27-fold covers : {675}*1350
   28-fold covers : {700}*1400
   29-fold covers : {725}*1450
   30-fold covers : {750}*1500
   31-fold covers : {775}*1550
   32-fold covers : {800}*1600
   33-fold covers : {825}*1650
   34-fold covers : {850}*1700
   35-fold covers : {875}*1750
   36-fold covers : {900}*1800
   37-fold covers : {925}*1850
   38-fold covers : {950}*1900
   39-fold covers : {975}*1950
   40-fold covers : {1000}*2000
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(25)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25);
s1 := Sym(25)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24);
poly := sub<Sym(25)|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 >;

References : None.
to this polytope