Polytope of Type {2,2,25}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,25}*200
if this polytope has a name.
Group : SmallGroup(200,13)
Rank : 4
Schlafli Type : {2,2,25}
Number of vertices, edges, etc : 2, 2, 25, 25
Order of s₀s₁s₂s₃ : 50
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,25,2} of size 400
   {2,2,25,10} of size 2000
Vertex Figure Of :
   {2,2,2,25} of size 400
   {3,2,2,25} of size 600
   {4,2,2,25} of size 800
   {5,2,2,25} of size 1000
   {6,2,2,25} of size 1200
   {7,2,2,25} of size 1400
   {8,2,2,25} of size 1600
   {9,2,2,25} of size 1800
   {10,2,2,25} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,25}*400, {2,2,50}*400
   3-fold covers : {6,2,25}*600, {2,2,75}*600
   4-fold covers : {8,2,25}*800, {2,2,100}*800, {2,4,50}*800, {4,2,50}*800
   5-fold covers : {2,2,125}*1000, {2,10,25}*1000, {10,2,25}*1000
   6-fold covers : {12,2,25}*1200, {4,2,75}*1200, {2,6,50}*1200, {6,2,50}*1200, {2,2,150}*1200
   7-fold covers : {14,2,25}*1400, {2,2,175}*1400
   8-fold covers : {16,2,25}*1600, {2,4,100}*1600, {4,2,100}*1600, {4,4,50}*1600, {2,2,200}*1600, {2,8,50}*1600, {8,2,50}*1600
   9-fold covers : {18,2,25}*1800, {2,2,225}*1800, {2,6,75}*1800, {6,2,75}*1800
   10-fold covers : {4,2,125}*2000, {2,2,250}*2000, {20,2,25}*2000, {4,10,25}*2000, {2,10,50}*2000a, {2,10,50}*2000b, {10,2,50}*2000
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27)(28,29);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(1,2);
s1 := Sym(29)!(3,4);
s2 := Sym(29)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25)(26,27)(28,29);
s3 := Sym(29)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
poly := sub<Sym(29)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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