Polytope of Type {6,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,5}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 4
Schlafli Type : {6,2,5}
Number of vertices, edges, etc : 6, 6, 5, 5
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,5,2} of size 240
   {6,2,5,3} of size 720
   {6,2,5,5} of size 720
   {6,2,5,10} of size 1200
   {6,2,5,4} of size 1440
   {6,2,5,6} of size 1440
   {6,2,5,3} of size 1440
   {6,2,5,5} of size 1440
   {6,2,5,6} of size 1440
   {6,2,5,6} of size 1440
   {6,2,5,10} of size 1440
   {6,2,5,10} of size 1440
   {6,2,5,4} of size 1920
   {6,2,5,5} of size 1920
Vertex Figure Of :
   {2,6,2,5} of size 240
   {3,6,2,5} of size 360
   {4,6,2,5} of size 480
   {3,6,2,5} of size 480
   {4,6,2,5} of size 480
   {4,6,2,5} of size 480
   {4,6,2,5} of size 720
   {6,6,2,5} of size 720
   {6,6,2,5} of size 720
   {6,6,2,5} of size 720
   {8,6,2,5} of size 960
   {4,6,2,5} of size 960
   {6,6,2,5} of size 960
   {9,6,2,5} of size 1080
   {3,6,2,5} of size 1080
   {6,6,2,5} of size 1080
   {4,6,2,5} of size 1200
   {5,6,2,5} of size 1200
   {6,6,2,5} of size 1200
   {5,6,2,5} of size 1200
   {5,6,2,5} of size 1200
   {10,6,2,5} of size 1200
   {12,6,2,5} of size 1440
   {12,6,2,5} of size 1440
   {12,6,2,5} of size 1440
   {3,6,2,5} of size 1440
   {12,6,2,5} of size 1440
   {4,6,2,5} of size 1440
   {14,6,2,5} of size 1680
   {15,6,2,5} of size 1800
   {16,6,2,5} of size 1920
   {4,6,2,5} of size 1920
   {6,6,2,5} of size 1920
   {3,6,2,5} of size 1920
   {8,6,2,5} of size 1920
   {4,6,2,5} of size 1920
   {12,6,2,5} of size 1920
   {8,6,2,5} of size 1920
   {12,6,2,5} of size 1920
   {6,6,2,5} of size 1920
   {8,6,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,5}*60
   3-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,5}*240, {6,2,10}*240
   3-fold covers : {18,2,5}*360, {6,2,15}*360
   4-fold covers : {24,2,5}*480, {12,2,10}*480, {6,2,20}*480, {6,4,10}*480
   5-fold covers : {6,2,25}*600, {6,10,5}*600, {30,2,5}*600
   6-fold covers : {36,2,5}*720, {18,2,10}*720, {12,2,15}*720, {6,6,10}*720a, {6,6,10}*720c, {6,2,30}*720
   7-fold covers : {42,2,5}*840, {6,2,35}*840
   8-fold covers : {48,2,5}*960, {12,2,20}*960, {12,4,10}*960, {6,4,20}*960, {24,2,10}*960, {6,2,40}*960, {6,8,10}*960, {6,4,10}*960
   9-fold covers : {54,2,5}*1080, {6,2,45}*1080, {18,2,15}*1080, {6,6,15}*1080a, {6,6,15}*1080b
   10-fold covers : {12,2,25}*1200, {6,2,50}*1200, {12,10,5}*1200, {60,2,5}*1200, {6,10,10}*1200a, {6,10,10}*1200b, {30,2,10}*1200
   11-fold covers : {66,2,5}*1320, {6,2,55}*1320
   12-fold covers : {72,2,5}*1440, {36,2,10}*1440, {18,2,20}*1440, {18,4,10}*1440, {24,2,15}*1440, {6,12,10}*1440a, {12,6,10}*1440a, {12,6,10}*1440b, {6,6,20}*1440a, {6,6,20}*1440c, {6,12,10}*1440c, {12,2,30}*1440, {6,2,60}*1440, {6,4,30}*1440, {6,6,15}*1440, {6,4,15}*1440
   13-fold covers : {78,2,5}*1560, {6,2,65}*1560
   14-fold covers : {84,2,5}*1680, {12,2,35}*1680, {6,14,10}*1680, {42,2,10}*1680, {6,2,70}*1680
   15-fold covers : {18,2,25}*1800, {6,2,75}*1800, {18,10,5}*1800, {90,2,5}*1800, {6,10,15}*1800, {30,2,15}*1800
   16-fold covers : {96,2,5}*1920, {12,4,20}*1920, {12,8,10}*1920a, {6,8,20}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {12,8,10}*1920b, {6,8,20}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {12,4,10}*1920a, {6,4,20}*1920a, {12,2,40}*1920, {24,2,20}*1920, {6,16,10}*1920, {48,2,10}*1920, {6,2,80}*1920, {12,4,10}*1920b, {6,4,20}*1920b, {6,4,10}*1920, {12,4,10}*1920c, {6,8,10}*1920a, {6,8,10}*1920b, {6,4,5}*1920
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11);;
s3 := ( 7, 8)( 9,10);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!(3,4)(5,6);
s1 := Sym(11)!(1,5)(2,3)(4,6);
s2 := Sym(11)!( 8, 9)(10,11);
s3 := Sym(11)!( 7, 8)( 9,10);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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