Polytope of Type {3,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,10}*300
Also Known As : {3,10}₆. if this polytope has another name.
Group : SmallGroup(300,25)
Rank : 3
Schlafli Type : {3,10}
Number of vertices, edges, etc : 15, 75, 50
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {3,10,2} of size 600
   {3,10,4} of size 1200
   {3,10,5} of size 1500
   {3,10,6} of size 1800
Vertex Figure Of :
   {2,3,10} of size 600
   {4,3,10} of size 1200
   {6,3,10} of size 1800
Quotients (Maximal Quotients in Boldface) :
   25-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,10}*600b
   3-fold covers : {9,10}*900, {3,30}*900
   4-fold covers : {12,10}*1200a, {6,20}*1200b, {3,20}*1200
   5-fold covers : {3,10}*1500, {15,10}*1500a, {15,10}*1500b, {15,10}*1500c, {15,10}*1500d, {15,10}*1500f, {15,10}*1500g
   6-fold covers : {18,10}*1800b, {6,30}*1800a, {6,30}*1800d
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, 7)( 3,13)( 4,19)( 5,25)( 6,21)( 9,14)(10,20)(11,16)(12,22)(18,23);;
s2 := ( 1, 2)( 3, 5)( 6,22)( 7,21)( 8,25)( 9,24)(10,23)(11,17)(12,16)(13,20)
(14,19)(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, s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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, 7)( 3,13)( 4,19)( 5,25)( 6,21)( 9,14)(10,20)(11,16)(12,22)
(18,23);
s2 := Sym(25)!( 1, 2)( 3, 5)( 6,22)( 7,21)( 8,25)( 9,24)(10,23)(11,17)(12,16)
(13,20)(14,19)(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, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope