Polytope of Type {5,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6}*120b
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 3
Schlafli Type : {5,6}
Number of vertices, edges, etc : 10, 30, 12
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {5,6,2} of size 240
Vertex Figure Of :
   {2,5,6} of size 240
   {4,5,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6}*240b, {10,6}*240e, {10,6}*240f
   3-fold covers : {15,6}*360
   4-fold covers : {20,6}*480a, {20,6}*480b, {5,12}*480, {10,6}*480c
   5-fold covers : {5,6}*600
   6-fold covers : {10,6}*720c, {15,6}*720c, {15,6}*720d, {30,6}*720a, {30,6}*720b
   7-fold covers : {35,6}*840
   8-fold covers : {40,6}*960a, {40,6}*960b, {10,12}*960c, {20,6}*960c, {10,12}*960d, {20,6}*960d, {10,6}*960b
   9-fold covers : {45,6}*1080
   10-fold covers : {5,6}*1200b, {5,30}*1200b, {10,6}*1200a, {10,6}*1200b, {10,30}*1200c
   11-fold covers : {55,6}*1320
   12-fold covers : {60,6}*1440a, {60,6}*1440b, {15,12}*1440a, {15,12}*1440b, {15,12}*1440d, {10,6}*1440f, {30,6}*1440e, {30,6}*1440f
   13-fold covers : {65,6}*1560
   14-fold covers : {10,42}*1680c, {35,6}*1680c, {70,6}*1680a, {70,6}*1680b
   15-fold covers : {15,6}*1800
   16-fold covers : {80,6}*1920a, {80,6}*1920b, {20,12}*1920g, {10,24}*1920d, {40,6}*1920f, {10,12}*1920c, {20,6}*1920d, {20,12}*1920k, {20,12}*1920l, {20,12}*1920m, {10,24}*1920f, {40,6}*1920h, {5,6}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope