Polytope of Type {10,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,5}*500
if this polytope has a name.
Group : SmallGroup(500,27)
Rank : 3
Schlafli Type : {10,5}
Number of vertices, edges, etc : 50, 125, 25
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,5,2} of size 1000
Vertex Figure Of :
   {2,10,5} of size 1000
   {4,10,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {10,5}*100
   25-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,10}*1000b
   3-fold covers : {10,15}*1500e
   4-fold covers : {10,20}*2000a, {20,10}*2000c
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1> of order 5.
      9 facets:
         5 of {2}*4
         4 of {10}*20
      10 vertex figures:
         10 of {5}*10

Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {10,5}

Twisty Puzzle