Polytope of Type {10,3}

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