Polytope of Type {6,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*300
Also Known As : {6,3}_(5,0), {6,3}₁₀. if this polytope has another name.
Group : SmallGroup(300,25)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 50, 75, 25
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,3,2} of size 600
Vertex Figure Of :
   {2,6,3} of size 600
   {4,6,3} of size 1200
   {6,6,3} of size 1800
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*600a
   3-fold covers : {6,3}*900
   4-fold covers : {6,12}*1200a, {12,6}*1200b, {6,3}*1200
   5-fold covers : {6,15}*1500a, {30,3}*1500, {6,15}*1500b
   6-fold covers : {6,6}*1800b, {6,6}*1800c
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 5.
      5 facets:
         5 of {6}*12
      10 vertex figures:
         10 of {3}*6

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,3}

Twisty Puzzle