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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,10,5}*1000
if this polytope has a name.
Group : SmallGroup(1000,106)
Rank : 5
Schlafli Type : {2,5,10,5}
Number of vertices, edges, etc : 2, 5, 25, 25, 5
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,10,5,2} of size 2000
Vertex Figure Of :
   {2,2,5,10,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,5,2,5}*200
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,5,10,10}*2000a, {2,10,10,5}*2000a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope