Polytope of Type {25,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25,2}*100
if this polytope has a name.
Group : SmallGroup(100,4)
Rank : 3
Schlafli Type : {25,2}
Number of vertices, edges, etc : 25, 25, 2
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 :
   {25,2,2} of size 200
   {25,2,3} of size 300
   {25,2,4} of size 400
   {25,2,5} of size 500
   {25,2,6} of size 600
   {25,2,7} of size 700
   {25,2,8} of size 800
   {25,2,9} of size 900
   {25,2,10} of size 1000
   {25,2,11} of size 1100
   {25,2,12} of size 1200
   {25,2,13} of size 1300
   {25,2,14} of size 1400
   {25,2,15} of size 1500
   {25,2,16} of size 1600
   {25,2,17} of size 1700
   {25,2,18} of size 1800
   {25,2,19} of size 1900
   {25,2,20} of size 2000
Vertex Figure Of :
   {2,25,2} of size 200
   {10,25,2} of size 1000
   {4,25,2} of size 1600
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {50,2}*200
   3-fold covers : {75,2}*300
   4-fold covers : {100,2}*400, {50,4}*400
   5-fold covers : {125,2}*500, {25,10}*500
   6-fold covers : {50,6}*600, {150,2}*600
   7-fold covers : {175,2}*700
   8-fold covers : {100,4}*800, {200,2}*800, {50,8}*800
   9-fold covers : {225,2}*900, {75,6}*900
   10-fold covers : {250,2}*1000, {50,10}*1000a, {50,10}*1000b
   11-fold covers : {275,2}*1100
   12-fold covers : {50,12}*1200, {100,6}*1200a, {300,2}*1200, {150,4}*1200a, {75,6}*1200, {75,4}*1200
   13-fold covers : {325,2}*1300
   14-fold covers : {50,14}*1400, {350,2}*1400
   15-fold covers : {375,2}*1500, {75,10}*1500
   16-fold covers : {200,4}*1600a, {100,4}*1600, {200,4}*1600b, {100,8}*1600a, {100,8}*1600b, {400,2}*1600, {50,16}*1600, {25,4}*1600
   17-fold covers : {425,2}*1700
   18-fold covers : {50,18}*1800, {450,2}*1800, {150,6}*1800a, {150,6}*1800b, {150,6}*1800c
   19-fold covers : {475,2}*1900
   20-fold covers : {500,2}*2000, {250,4}*2000, {50,20}*2000a, {100,10}*2000a, {100,10}*2000b, {50,20}*2000b
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);;
s2 := (26,27);;
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*s2*s0*s2, s1*s2*s1*s2, 
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(27)!( 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(27)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24);
s2 := Sym(27)!(26,27);
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*s2*s0*s2, s1*s2*s1*s2, 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 >;

to this polytope