Polytope of Type {5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10}*120b
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 3
Schlafli Type : {5,10}
Number of vertices, edges, etc : 6, 30, 12
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,10,2} of size 240
   {5,10,4} of size 480
   {5,10,6} of size 720
   {5,10,8} of size 960
   {5,10,10} of size 1200
   {5,10,12} of size 1440
   {5,10,14} of size 1680
   {5,10,16} of size 1920
Vertex Figure Of :
   {2,5,10} of size 240
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,10}*240, {10,10}*240a, {10,10}*240b
   4-fold covers : {10,20}*480a, {10,20}*480b, {5,20}*480, {10,10}*480
   6-fold covers : {10,30}*720a, {15,10}*720
   8-fold covers : {10,40}*960a, {10,40}*960b, {10,20}*960a, {20,10}*960a, {10,20}*960b, {20,10}*960b, {10,10}*960
   10-fold covers : {5,10}*1200a, {5,10}*1200b, {10,10}*1200a
   12-fold covers : {10,60}*1440a, {10,60}*1440b, {15,20}*1440a, {10,30}*1440, {30,10}*1440
   14-fold covers : {10,70}*1680a, {35,10}*1680
   16-fold covers : {10,80}*1920a, {10,80}*1920b, {20,20}*1920a, {10,40}*1920a, {40,10}*1920a, {10,20}*1920, {20,10}*1920, {20,20}*1920b, {20,20}*1920c, {20,20}*1920d, {10,40}*1920b, {40,10}*1920b, {5,10}*1920a
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);;
s1 := ( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12);;
s2 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);;
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*s0*s1*s0*s1, 
s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);
s1 := Sym(12)!( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12);
s2 := Sym(12)!( 2, 9)( 4,12)( 5, 7)( 6, 8);
poly := sub<Sym(12)|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*s0*s1*s0*s1, 
s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0 >;

References : None.
to this polytope