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Polytope of Type {2,21,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,21,4,2}*672
if this polytope has a name.
Group : SmallGroup(672,1263)
Rank : 5
Schlafli Type : {2,21,4,2}
Number of vertices, edges, etc : 2, 21, 42, 4, 2
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,21,4,2,2} of size 1344
Vertex Figure Of :
   {2,2,21,4,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,21,4,2}*1344, {2,42,4,2}*1344b, {2,42,4,2}*1344c
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);;
s4 := (31,32);;
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*s1*s0*s1, 
s0*s2*s0*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, 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(32)!(1,2);
s1 := Sym(32)!( 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(32)!( 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(32)!( 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);
s4 := Sym(32)!(31,32);
poly := sub<Sym(32)|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*s1*s0*s1, s0*s2*s0*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, 
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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