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Polytope of Type {10,2,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,6,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {10,2,6,4}
Number of vertices, edges, etc : 10, 10, 12, 24, 8
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,6,4}*960, {10,2,3,4}*960, {10,2,6,4}*960b, {10,2,6,4}*960c
   4-fold quotients : {5,2,3,4}*480, {5,2,6,4}*480b, {5,2,6,4}*480c, {10,2,3,4}*480, {10,2,6,2}*480
   5-fold quotients : {2,2,6,4}*384
   8-fold quotients : {5,2,3,4}*240, {5,2,6,2}*240, {10,2,3,2}*240
   10-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
   12-fold quotients : {10,2,2,2}*160
   16-fold quotients : {5,2,3,2}*120
   20-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
   24-fold quotients : {5,2,2,2}*80
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (18,19)(21,22)(23,24)(25,26);;
s3 := (11,12)(13,15)(14,21)(16,18)(17,25)(19,22)(20,23)(24,26);;
s4 := (11,17)(12,20)(13,14)(15,16)(18,24)(19,23)(21,26)(22,25);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
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(26)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(26)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(26)!(18,19)(21,22)(23,24)(25,26);
s3 := Sym(26)!(11,12)(13,15)(14,21)(16,18)(17,25)(19,22)(20,23)(24,26);
s4 := Sym(26)!(11,17)(12,20)(13,14)(15,16)(18,24)(19,23)(21,26)(22,25);
poly := sub<Sym(26)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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