Polytope of Type {25,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25,2,2}*200
if this polytope has a name.
Group : SmallGroup(200,13)
Rank : 4
Schlafli Type : {25,2,2}
Number of vertices, edges, etc : 25, 25, 2, 2
Order of s₀s₁s₂s₃ : 50
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {25,2,2,2} of size 400
   {25,2,2,3} of size 600
   {25,2,2,4} of size 800
   {25,2,2,5} of size 1000
   {25,2,2,6} of size 1200
   {25,2,2,7} of size 1400
   {25,2,2,8} of size 1600
   {25,2,2,9} of size 1800
   {25,2,2,10} of size 2000
Vertex Figure Of :
   {2,25,2,2} of size 400
   {10,25,2,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {25,2,4}*400, {50,2,2}*400
   3-fold covers : {25,2,6}*600, {75,2,2}*600
   4-fold covers : {25,2,8}*800, {100,2,2}*800, {50,2,4}*800, {50,4,2}*800
   5-fold covers : {125,2,2}*1000, {25,2,10}*1000, {25,10,2}*1000
   6-fold covers : {25,2,12}*1200, {75,2,4}*1200, {50,2,6}*1200, {50,6,2}*1200, {150,2,2}*1200
   7-fold covers : {25,2,14}*1400, {175,2,2}*1400
   8-fold covers : {25,2,16}*1600, {100,4,2}*1600, {100,2,4}*1600, {50,4,4}*1600, {200,2,2}*1600, {50,2,8}*1600, {50,8,2}*1600
   9-fold covers : {25,2,18}*1800, {225,2,2}*1800, {75,2,6}*1800, {75,6,2}*1800
   10-fold covers : {125,2,4}*2000, {250,2,2}*2000, {25,2,20}*2000, {25,10,4}*2000, {50,2,10}*2000, {50,10,2}*2000a, {50,10,2}*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);;
s3 := (28,29);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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(29)!( 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(29)!( 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(29)!(26,27);
s3 := Sym(29)!(28,29);
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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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 >;

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