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

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