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Polytope of Type {15,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,2,6}*360
if this polytope has a name.
Group : SmallGroup(360,154)
Rank : 4
Schlafli Type : {15,2,6}
Number of vertices, edges, etc : 15, 15, 6, 6
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,2,6,2} of size 720
   {15,2,6,3} of size 1080
   {15,2,6,4} of size 1440
   {15,2,6,3} of size 1440
   {15,2,6,4} of size 1440
   {15,2,6,4} of size 1440
Vertex Figure Of :
   {2,15,2,6} of size 720
   {4,15,2,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,2,3}*180
   3-fold quotients : {5,2,6}*120, {15,2,2}*120
   5-fold quotients : {3,2,6}*72
   6-fold quotients : {5,2,3}*60
   9-fold quotients : {5,2,2}*40
   10-fold quotients : {3,2,3}*36
   15-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,2,12}*720, {30,2,6}*720
   3-fold covers : {45,2,6}*1080, {15,2,18}*1080, {15,6,6}*1080a, {15,6,6}*1080b
   4-fold covers : {15,2,24}*1440, {30,2,12}*1440, {60,2,6}*1440, {30,4,6}*1440, {15,4,6}*1440
   5-fold covers : {75,2,6}*1800, {15,10,6}*1800, {15,2,30}*1800
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s2 := (18,19)(20,21);;
s3 := (16,20)(17,18)(19,21);;
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*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*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(21)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(21)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s2 := Sym(21)!(18,19)(20,21);
s3 := Sym(21)!(16,20)(17,18)(19,21);
poly := sub<Sym(21)|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*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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