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Polytope of Type {4,2,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,21}*336
if this polytope has a name.
Group : SmallGroup(336,198)
Rank : 4
Schlafli Type : {4,2,21}
Number of vertices, edges, etc : 4, 4, 21, 21
Order of s0s1s2s3 : 84
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,21,2} of size 672
   {4,2,21,4} of size 1344
Vertex Figure Of :
   {2,4,2,21} of size 672
   {3,4,2,21} of size 1008
   {4,4,2,21} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,21}*168
   3-fold quotients : {4,2,7}*112
   6-fold quotients : {2,2,7}*56
   7-fold quotients : {4,2,3}*48
   14-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,21}*672, {4,2,42}*672
   3-fold covers : {4,2,63}*1008, {12,2,21}*1008, {4,6,21}*1008
   4-fold covers : {16,2,21}*1344, {4,2,84}*1344, {4,4,42}*1344, {8,2,42}*1344, {4,4,21}*1344b
   5-fold covers : {20,2,21}*1680, {4,2,105}*1680
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24);;
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*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*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(25)!(2,3);
s1 := Sym(25)!(1,2)(3,4);
s2 := Sym(25)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25);
s3 := Sym(25)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24);
poly := sub<Sym(25)|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*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*s2*s3 >; 
 

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