Polytope of Type {25,2,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25,2,2,2}*400
if this polytope has a name.
Group : SmallGroup(400,54)
Rank : 5
Schlafli Type : {25,2,2,2}
Number of vertices, edges, etc : 25, 25, 2, 2, 2
Order of s₀s₁s₂s₃s₄ : 50
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {25,2,2,2,2} of size 800
   {25,2,2,2,3} of size 1200
   {25,2,2,2,4} of size 1600
   {25,2,2,2,5} of size 2000
Vertex Figure Of :
   {2,25,2,2,2} of size 800
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {25,2,2,4}*800, {25,2,4,2}*800, {50,2,2,2}*800
   3-fold covers : {25,2,2,6}*1200, {25,2,6,2}*1200, {75,2,2,2}*1200
   4-fold covers : {25,2,4,4}*1600, {25,2,2,8}*1600, {25,2,8,2}*1600, {100,2,2,2}*1600, {50,2,2,4}*1600, {50,2,4,2}*1600, {50,4,2,2}*1600
   5-fold covers : {125,2,2,2}*2000, {25,2,2,10}*2000, {25,2,10,2}*2000, {25,10,2,2}*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);;
s2 := (26,27);;
s3 := (28,29);;
s4 := (30,31);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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(31)!( 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(31)!( 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(31)!(26,27);
s3 := Sym(31)!(28,29);
s4 := Sym(31)!(30,31);
poly := sub<Sym(31)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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