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Polytope of Type {3,2,17}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,17}*204
if this polytope has a name.
Group : SmallGroup(204,7)
Rank : 4
Schlafli Type : {3,2,17}
Number of vertices, edges, etc : 3, 3, 17, 17
Order of s0s1s2s3 : 51
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,17,2} of size 408
Vertex Figure Of :
   {2,3,2,17} of size 408
   {3,3,2,17} of size 816
   {4,3,2,17} of size 816
   {6,3,2,17} of size 1224
   {4,3,2,17} of size 1632
   {6,3,2,17} of size 1632
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,34}*408, {6,2,17}*408
   3-fold covers : {9,2,17}*612, {3,2,51}*612
   4-fold covers : {12,2,17}*816, {3,2,68}*816, {6,2,34}*816
   5-fold covers : {15,2,17}*1020, {3,2,85}*1020
   6-fold covers : {9,2,34}*1224, {18,2,17}*1224, {3,6,34}*1224, {3,2,102}*1224, {6,2,51}*1224
   7-fold covers : {21,2,17}*1428, {3,2,119}*1428
   8-fold covers : {24,2,17}*1632, {3,2,136}*1632, {12,2,34}*1632, {6,2,68}*1632, {6,4,34}*1632, {3,4,34}*1632
   9-fold covers : {27,2,17}*1836, {3,2,153}*1836, {9,2,51}*1836, {3,6,51}*1836
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
s3 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, 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*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!(2,3);
s1 := Sym(20)!(1,2);
s2 := Sym(20)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);
s3 := Sym(20)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
poly := sub<Sym(20)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, 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*s2*s3*s2*s3 >; 
 

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