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Polytope of Type {5,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,3,2}*120
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 4
Schlafli Type : {5,3,2}
Number of vertices, edges, etc : 10, 15, 6, 2
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Locally Projective
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,3,2,2} of size 240
   {5,3,2,3} of size 360
   {5,3,2,4} of size 480
   {5,3,2,5} of size 600
   {5,3,2,6} of size 720
   {5,3,2,7} of size 840
   {5,3,2,8} of size 960
   {5,3,2,9} of size 1080
   {5,3,2,10} of size 1200
   {5,3,2,11} of size 1320
   {5,3,2,12} of size 1440
   {5,3,2,13} of size 1560
   {5,3,2,14} of size 1680
   {5,3,2,15} of size 1800
   {5,3,2,16} of size 1920
Vertex Figure Of :
   {2,5,3,2} of size 240
   {3,5,3,2} of size 1320
   {4,5,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,3,2}*240, {5,6,2}*240b, {5,6,2}*240c, {10,3,2}*240a, {10,3,2}*240b
   4-fold covers : {5,6,4}*480b, {5,6,2}*480b, {10,3,2}*480, {10,6,2}*480c, {10,6,2}*480d, {10,6,2}*480e, {10,6,2}*480f
   6-fold covers : {5,6,6}*720b, {10,3,2}*720, {15,3,2}*720, {15,6,2}*720
   8-fold covers : {5,6,8}*960b, {5,6,4}*960b, {10,6,4}*960c, {10,6,4}*960d, {10,12,2}*960c, {10,12,2}*960d, {20,6,2}*960a, {20,6,2}*960b, {5,12,2}*960, {20,3,2}*960, {10,6,2}*960c
   10-fold covers : {5,6,10}*1200b, {5,6,2}*1200, {5,15,2}*1200, {10,15,2}*1200
   12-fold covers : {5,6,12}*1440b, {5,6,6}*1440b, {10,6,6}*1440c, {10,6,6}*1440d, {10,3,2}*1440b, {10,6,2}*1440b, {10,6,2}*1440c, {15,6,2}*1440c, {15,6,2}*1440d, {30,3,2}*1440, {30,6,2}*1440a, {30,6,2}*1440b
   14-fold covers : {5,6,14}*1680b, {10,21,2}*1680, {35,6,2}*1680
   16-fold covers : {5,6,16}*1920b, {10,12,4}*1920f, {10,12,4}*1920g, {5,6,8}*1920b, {10,6,8}*1920e, {10,6,8}*1920f, {10,24,2}*1920c, {10,24,2}*1920d, {40,6,2}*1920d, {40,6,2}*1920e, {10,6,4}*1920d, {10,12,2}*1920c, {20,6,2}*1920c, {5,12,4}*1920, {10,12,2}*1920e, {20,6,2}*1920e, {10,6,2}*1920b, {5,3,4}*1920, {5,6,2}*1920
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,5)(3,4);;
s3 := (6,7);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(7)!(2,3)(4,5);
s1 := Sym(7)!(1,2)(3,4);
s2 := Sym(7)!(2,5)(3,4);
s3 := Sym(7)!(6,7);
poly := sub<Sym(7)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >; 
 

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