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Polytope of Type {2,2,15,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,15,2}*240
if this polytope has a name.
Group : SmallGroup(240,207)
Rank : 5
Schlafli Type : {2,2,15,2}
Number of vertices, edges, etc : 2, 2, 15, 15, 2
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,15,2,2} of size 480
   {2,2,15,2,3} of size 720
   {2,2,15,2,4} of size 960
   {2,2,15,2,5} of size 1200
   {2,2,15,2,6} of size 1440
   {2,2,15,2,7} of size 1680
   {2,2,15,2,8} of size 1920
Vertex Figure Of :
   {2,2,2,15,2} of size 480
   {3,2,2,15,2} of size 720
   {4,2,2,15,2} of size 960
   {5,2,2,15,2} of size 1200
   {6,2,2,15,2} of size 1440
   {7,2,2,15,2} of size 1680
   {8,2,2,15,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,5,2}*80
   5-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,15,2}*480, {2,2,30,2}*480
   3-fold covers : {2,2,45,2}*720, {2,2,15,6}*720, {2,6,15,2}*720, {6,2,15,2}*720
   4-fold covers : {8,2,15,2}*960, {2,2,60,2}*960, {2,2,30,4}*960a, {2,4,30,2}*960a, {4,2,30,2}*960, {2,2,15,4}*960, {2,4,15,2}*960
   5-fold covers : {2,2,75,2}*1200, {2,2,15,10}*1200, {2,10,15,2}*1200, {10,2,15,2}*1200
   6-fold covers : {4,2,45,2}*1440, {2,2,90,2}*1440, {12,2,15,2}*1440, {4,2,15,6}*1440, {4,6,15,2}*1440, {2,2,30,6}*1440b, {2,2,30,6}*1440c, {2,6,30,2}*1440b, {2,6,30,2}*1440c, {6,2,30,2}*1440
   7-fold covers : {14,2,15,2}*1680, {2,2,105,2}*1680
   8-fold covers : {16,2,15,2}*1920, {4,4,30,2}*1920, {2,2,60,4}*1920a, {2,4,60,2}*1920a, {4,2,30,4}*1920a, {2,4,30,4}*1920a, {4,2,60,2}*1920, {2,2,30,8}*1920, {2,8,30,2}*1920, {8,2,30,2}*1920, {2,2,120,2}*1920, {4,2,15,4}*1920, {4,4,15,2}*1920b, {2,2,15,8}*1920, {2,8,15,2}*1920, {2,2,30,4}*1920, {2,4,30,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s4 := (20,21);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!(1,2);
s1 := Sym(21)!(3,4);
s2 := Sym(21)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
s3 := Sym(21)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s4 := Sym(21)!(20,21);
poly := sub<Sym(21)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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