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Polytope of Type {3,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,20}*240
if this polytope has a name.
Group : SmallGroup(240,137)
Rank : 4
Schlafli Type : {3,2,20}
Number of vertices, edges, etc : 3, 3, 20, 20
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,20,2} of size 480
   {3,2,20,4} of size 960
   {3,2,20,6} of size 1440
   {3,2,20,6} of size 1440
   {3,2,20,8} of size 1920
   {3,2,20,8} of size 1920
   {3,2,20,4} of size 1920
Vertex Figure Of :
   {2,3,2,20} of size 480
   {3,3,2,20} of size 960
   {4,3,2,20} of size 960
   {6,3,2,20} of size 1440
   {4,3,2,20} of size 1920
   {6,3,2,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,10}*120
   4-fold quotients : {3,2,5}*60
   5-fold quotients : {3,2,4}*48
   10-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,40}*480, {6,2,20}*480
   3-fold covers : {9,2,20}*720, {3,6,20}*720, {3,2,60}*720
   4-fold covers : {3,2,80}*960, {12,2,20}*960, {6,4,20}*960, {6,2,40}*960, {3,4,20}*960
   5-fold covers : {3,2,100}*1200, {15,2,20}*1200
   6-fold covers : {9,2,40}*1440, {18,2,20}*1440, {3,6,40}*1440, {3,2,120}*1440, {6,6,20}*1440a, {6,6,20}*1440c, {6,2,60}*1440
   7-fold covers : {21,2,20}*1680, {3,2,140}*1680
   8-fold covers : {3,2,160}*1920, {12,4,20}*1920, {6,8,20}*1920a, {6,4,40}*1920a, {6,8,20}*1920b, {6,4,40}*1920b, {6,4,20}*1920a, {12,2,40}*1920, {24,2,20}*1920, {6,2,80}*1920, {3,8,20}*1920, {3,4,40}*1920, {6,4,20}*1920b
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23);;
s3 := ( 4,10)( 5, 7)( 6,16)( 8,18)( 9,12)(11,14)(13,22)(15,19)(17,20)(21,23);;
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*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(23)!(2,3);
s1 := Sym(23)!(1,2);
s2 := Sym(23)!( 5, 6)( 7, 8)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23);
s3 := Sym(23)!( 4,10)( 5, 7)( 6,16)( 8,18)( 9,12)(11,14)(13,22)(15,19)(17,20)
(21,23);
poly := sub<Sym(23)|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*s2*s3*s2*s3*s2*s3 >; 
 

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