Polytope of Type {5,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,6}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 4
Schlafli Type : {5,2,6}
Number of vertices, edges, etc : 5, 5, 6, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,6,2} of size 240
   {5,2,6,3} of size 360
   {5,2,6,4} of size 480
   {5,2,6,3} of size 480
   {5,2,6,4} of size 480
   {5,2,6,4} of size 480
   {5,2,6,4} of size 720
   {5,2,6,6} of size 720
   {5,2,6,6} of size 720
   {5,2,6,6} of size 720
   {5,2,6,8} of size 960
   {5,2,6,4} of size 960
   {5,2,6,6} of size 960
   {5,2,6,9} of size 1080
   {5,2,6,3} of size 1080
   {5,2,6,6} of size 1080
   {5,2,6,4} of size 1200
   {5,2,6,5} of size 1200
   {5,2,6,6} of size 1200
   {5,2,6,5} of size 1200
   {5,2,6,5} of size 1200
   {5,2,6,10} of size 1200
   {5,2,6,12} of size 1440
   {5,2,6,12} of size 1440
   {5,2,6,12} of size 1440
   {5,2,6,3} of size 1440
   {5,2,6,12} of size 1440
   {5,2,6,4} of size 1440
   {5,2,6,14} of size 1680
   {5,2,6,15} of size 1800
   {5,2,6,16} of size 1920
   {5,2,6,4} of size 1920
   {5,2,6,6} of size 1920
   {5,2,6,3} of size 1920
   {5,2,6,8} of size 1920
   {5,2,6,4} of size 1920
   {5,2,6,12} of size 1920
   {5,2,6,8} of size 1920
   {5,2,6,12} of size 1920
   {5,2,6,6} of size 1920
   {5,2,6,8} of size 1920
Vertex Figure Of :
   {2,5,2,6} of size 240
   {3,5,2,6} of size 720
   {5,5,2,6} of size 720
   {10,5,2,6} of size 1200
   {4,5,2,6} of size 1440
   {6,5,2,6} of size 1440
   {3,5,2,6} of size 1440
   {5,5,2,6} of size 1440
   {6,5,2,6} of size 1440
   {6,5,2,6} of size 1440
   {10,5,2,6} of size 1440
   {10,5,2,6} of size 1440
   {4,5,2,6} of size 1920
   {5,5,2,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,3}*60
   3-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,12}*240, {10,2,6}*240
   3-fold covers : {5,2,18}*360, {15,2,6}*360
   4-fold covers : {5,2,24}*480, {10,2,12}*480, {20,2,6}*480, {10,4,6}*480
   5-fold covers : {25,2,6}*600, {5,10,6}*600, {5,2,30}*600
   6-fold covers : {5,2,36}*720, {10,2,18}*720, {15,2,12}*720, {10,6,6}*720a, {10,6,6}*720b, {30,2,6}*720
   7-fold covers : {5,2,42}*840, {35,2,6}*840
   8-fold covers : {5,2,48}*960, {20,2,12}*960, {10,4,12}*960, {20,4,6}*960, {10,2,24}*960, {40,2,6}*960, {10,8,6}*960, {10,4,6}*960
   9-fold covers : {5,2,54}*1080, {45,2,6}*1080, {15,2,18}*1080, {15,6,6}*1080a, {15,6,6}*1080b
   10-fold covers : {25,2,12}*1200, {50,2,6}*1200, {5,10,12}*1200, {5,2,60}*1200, {10,10,6}*1200a, {10,10,6}*1200c, {10,2,30}*1200
   11-fold covers : {5,2,66}*1320, {55,2,6}*1320
   12-fold covers : {5,2,72}*1440, {10,2,36}*1440, {20,2,18}*1440, {10,4,18}*1440, {15,2,24}*1440, {10,6,12}*1440a, {10,6,12}*1440b, {10,12,6}*1440a, {20,6,6}*1440a, {20,6,6}*1440c, {10,12,6}*1440c, {30,2,12}*1440, {60,2,6}*1440, {30,4,6}*1440, {15,6,6}*1440, {15,4,6}*1440
   13-fold covers : {5,2,78}*1560, {65,2,6}*1560
   14-fold covers : {5,2,84}*1680, {35,2,12}*1680, {10,14,6}*1680, {10,2,42}*1680, {70,2,6}*1680
   15-fold covers : {25,2,18}*1800, {75,2,6}*1800, {5,10,18}*1800, {5,2,90}*1800, {15,10,6}*1800, {15,2,30}*1800
   16-fold covers : {5,2,96}*1920, {20,4,12}*1920, {10,8,12}*1920a, {20,8,6}*1920a, {10,4,24}*1920a, {40,4,6}*1920a, {10,8,12}*1920b, {20,8,6}*1920b, {10,4,24}*1920b, {40,4,6}*1920b, {10,4,12}*1920a, {20,4,6}*1920a, {40,2,12}*1920, {20,2,24}*1920, {10,16,6}*1920, {10,2,48}*1920, {80,2,6}*1920, {10,4,12}*1920b, {20,4,6}*1920b, {10,4,6}*1920, {10,4,12}*1920c, {10,8,6}*1920a, {10,8,6}*1920b, {5,4,6}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(10,11);;
s3 := ( 6,10)( 7, 8)( 9,11);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(2,3)(4,5);
s1 := Sym(11)!(1,2)(3,4);
s2 := Sym(11)!( 8, 9)(10,11);
s3 := Sym(11)!( 6,10)( 7, 8)( 9,11);
poly := sub<Sym(11)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope