Polytope of Type {2,25}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,25}*100
if this polytope has a name.
Group : SmallGroup(100,4)
Rank : 3
Schlafli Type : {2,25}
Number of vertices, edges, etc : 2, 25, 25
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 :
   {2,25,2} of size 200
   {2,25,10} of size 1000
   {2,25,4} of size 1600
Vertex Figure Of :
   {2,2,25} of size 200
   {3,2,25} of size 300
   {4,2,25} of size 400
   {5,2,25} of size 500
   {6,2,25} of size 600
   {7,2,25} of size 700
   {8,2,25} of size 800
   {9,2,25} of size 900
   {10,2,25} of size 1000
   {11,2,25} of size 1100
   {12,2,25} of size 1200
   {13,2,25} of size 1300
   {14,2,25} of size 1400
   {15,2,25} of size 1500
   {16,2,25} of size 1600
   {17,2,25} of size 1700
   {18,2,25} of size 1800
   {19,2,25} of size 1900
   {20,2,25} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,50}*200
   3-fold covers : {2,75}*300
   4-fold covers : {2,100}*400, {4,50}*400
   5-fold covers : {2,125}*500, {10,25}*500
   6-fold covers : {6,50}*600, {2,150}*600
   7-fold covers : {2,175}*700
   8-fold covers : {4,100}*800, {2,200}*800, {8,50}*800
   9-fold covers : {2,225}*900, {6,75}*900
   10-fold covers : {2,250}*1000, {10,50}*1000a, {10,50}*1000b
   11-fold covers : {2,275}*1100
   12-fold covers : {12,50}*1200, {6,100}*1200a, {2,300}*1200, {4,150}*1200a, {6,75}*1200, {4,75}*1200
   13-fold covers : {2,325}*1300
   14-fold covers : {14,50}*1400, {2,350}*1400
   15-fold covers : {2,375}*1500, {10,75}*1500
   16-fold covers : {4,200}*1600a, {4,100}*1600, {4,200}*1600b, {8,100}*1600a, {8,100}*1600b, {2,400}*1600, {16,50}*1600, {4,25}*1600
   17-fold covers : {2,425}*1700
   18-fold covers : {18,50}*1800, {2,450}*1800, {6,150}*1800a, {6,150}*1800b, {6,150}*1800c
   19-fold covers : {2,475}*1900
   20-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 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25)(26,27);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(27)!(1,2);
s1 := Sym(27)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27);
s2 := Sym(27)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26);
poly := sub<Sym(27)|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 >;

to this polytope