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Polytope of Type {2,21,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,21,4}*336
if this polytope has a name.
Group : SmallGroup(336,215)
Rank : 4
Schlafli Type : {2,21,4}
Number of vertices, edges, etc : 2, 21, 42, 4
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,21,4,2} of size 672
Vertex Figure Of :
   {2,2,21,4} of size 672
   {3,2,21,4} of size 1008
   {4,2,21,4} of size 1344
   {5,2,21,4} of size 1680
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,21,4}*672, {2,42,4}*672b, {2,42,4}*672c
   3-fold covers : {2,63,4}*1008, {6,21,4}*1008
   4-fold covers : {2,84,4}*1344b, {2,84,4}*1344c, {4,42,4}*1344b, {2,21,8}*1344, {2,42,4}*1344, {4,21,4}*1344b
   5-fold covers : {2,105,4}*1680
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7,27)( 8,28)( 9,30)(10,29)(11,23)(12,24)(13,26)(14,25)(15,19)
(16,20)(17,22)(18,21);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,27)(12,29)(13,28)(14,30)(15,23)(16,25)
(17,24)(18,26)(20,21);;
s3 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(30)!(1,2);
s1 := Sym(30)!( 5, 6)( 7,27)( 8,28)( 9,30)(10,29)(11,23)(12,24)(13,26)(14,25)
(15,19)(16,20)(17,22)(18,21);
s2 := Sym(30)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,27)(12,29)(13,28)(14,30)(15,23)
(16,25)(17,24)(18,26)(20,21);
s3 := Sym(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30);
poly := sub<Sym(30)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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