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Polytope of Type {2,10,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,2,3}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 5
Schlafli Type : {2,10,2,3}
Number of vertices, edges, etc : 2, 10, 10, 3, 3
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,2,3,2} of size 480
   {2,10,2,3,3} of size 960
   {2,10,2,3,4} of size 960
   {2,10,2,3,6} of size 1440
   {2,10,2,3,4} of size 1920
   {2,10,2,3,6} of size 1920
Vertex Figure Of :
   {2,2,10,2,3} of size 480
   {3,2,10,2,3} of size 720
   {4,2,10,2,3} of size 960
   {5,2,10,2,3} of size 1200
   {6,2,10,2,3} of size 1440
   {7,2,10,2,3} of size 1680
   {8,2,10,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,2,3}*120
   5-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,20,2,3}*480, {4,10,2,3}*480, {2,10,2,6}*480
   3-fold covers : {2,10,2,9}*720, {2,10,6,3}*720, {6,10,2,3}*720, {2,30,2,3}*720
   4-fold covers : {4,20,2,3}*960, {2,40,2,3}*960, {8,10,2,3}*960, {2,10,2,12}*960, {2,20,2,6}*960, {2,10,4,6}*960, {4,10,2,6}*960, {2,10,4,3}*960
   5-fold covers : {2,50,2,3}*1200, {10,10,2,3}*1200a, {10,10,2,3}*1200b, {2,10,2,15}*1200
   6-fold covers : {2,20,2,9}*1440, {4,10,2,9}*1440, {2,10,2,18}*1440, {12,10,2,3}*1440, {6,20,2,3}*1440a, {2,20,6,3}*1440, {4,10,6,3}*1440, {2,60,2,3}*1440, {4,30,2,3}*1440a, {2,10,6,6}*1440a, {2,10,6,6}*1440b, {6,10,2,6}*1440, {2,30,2,6}*1440
   7-fold covers : {14,10,2,3}*1680, {2,10,2,21}*1680, {2,70,2,3}*1680
   8-fold covers : {8,20,2,3}*1920a, {4,40,2,3}*1920a, {8,20,2,3}*1920b, {4,40,2,3}*1920b, {4,20,2,3}*1920, {16,10,2,3}*1920, {2,80,2,3}*1920, {2,10,4,12}*1920, {2,20,4,6}*1920, {4,20,2,6}*1920, {4,10,4,6}*1920, {4,10,2,12}*1920, {2,20,2,12}*1920, {2,10,8,6}*1920, {8,10,2,6}*1920, {2,10,2,24}*1920, {2,40,2,6}*1920, {2,20,4,3}*1920, {4,10,4,3}*1920, {2,10,8,3}*1920, {2,10,4,6}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);;
s3 := (14,15);;
s4 := (13,14);;
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, 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*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(15)!(1,2);
s1 := Sym(15)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(15)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
s3 := Sym(15)!(14,15);
s4 := Sym(15)!(13,14);
poly := sub<Sym(15)|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, 
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*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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