Polytope of Type {2,5,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,10,2}*400
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 5
Schlafli Type : {2,5,10,2}
Number of vertices, edges, etc : 2, 5, 25, 10, 2
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,10,2,2} of size 800
   {2,5,10,2,3} of size 1200
   {2,5,10,2,4} of size 1600
   {2,5,10,2,5} of size 2000
Vertex Figure Of :
   {2,2,5,10,2} of size 800
   {3,2,5,10,2} of size 1200
   {4,2,5,10,2} of size 1600
   {5,2,5,10,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,5,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,5,10,4}*800, {2,10,10,2}*800c
   3-fold covers : {2,5,10,6}*1200, {2,15,10,2}*1200
   4-fold covers : {2,5,10,8}*1600, {2,20,10,2}*1600b, {4,10,10,2}*1600b, {2,10,10,4}*1600c, {2,10,20,2}*1600c
   5-fold covers : {2,25,10,2}*2000, {2,5,10,2}*2000, {2,5,10,10}*2000b, {10,5,10,2}*2000
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,20)(18,23)(19,22)
(24,27)(25,26);;
s2 := ( 3, 9)( 4, 6)( 5,16)( 7,18)( 8,12)(10,14)(11,20)(13,24)(15,19)(17,22)
(21,26)(23,25);;
s3 := ( 6, 7)( 9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s4 := (28,29);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(1,2);
s1 := Sym(29)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,20)(18,23)
(19,22)(24,27)(25,26);
s2 := Sym(29)!( 3, 9)( 4, 6)( 5,16)( 7,18)( 8,12)(10,14)(11,20)(13,24)(15,19)
(17,22)(21,26)(23,25);
s3 := Sym(29)!( 6, 7)( 9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27);
s4 := Sym(29)!(28,29);
poly := sub<Sym(29)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope