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Polytope of Type {21,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,2,2}*168
if this polytope has a name.
Group : SmallGroup(168,56)
Rank : 4
Schlafli Type : {21,2,2}
Number of vertices, edges, etc : 21, 21, 2, 2
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {21,2,2,2} of size 336
   {21,2,2,3} of size 504
   {21,2,2,4} of size 672
   {21,2,2,5} of size 840
   {21,2,2,6} of size 1008
   {21,2,2,7} of size 1176
   {21,2,2,8} of size 1344
   {21,2,2,9} of size 1512
   {21,2,2,10} of size 1680
   {21,2,2,11} of size 1848
Vertex Figure Of :
   {2,21,2,2} of size 336
   {4,21,2,2} of size 672
   {6,21,2,2} of size 1008
   {6,21,2,2} of size 1344
   {4,21,2,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {7,2,2}*56
   7-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {21,2,4}*336, {42,2,2}*336
   3-fold covers : {63,2,2}*504, {21,2,6}*504, {21,6,2}*504
   4-fold covers : {21,2,8}*672, {84,2,2}*672, {42,2,4}*672, {42,4,2}*672a, {21,4,2}*672
   5-fold covers : {21,2,10}*840, {105,2,2}*840
   6-fold covers : {63,2,4}*1008, {126,2,2}*1008, {21,2,12}*1008, {21,6,4}*1008, {42,2,6}*1008, {42,6,2}*1008b, {42,6,2}*1008c
   7-fold covers : {147,2,2}*1176, {21,2,14}*1176, {21,14,2}*1176
   8-fold covers : {21,2,16}*1344, {84,4,2}*1344a, {84,2,4}*1344, {42,4,4}*1344, {168,2,2}*1344, {42,2,8}*1344, {42,8,2}*1344, {21,4,4}*1344b, {21,8,2}*1344, {42,4,2}*1344
   9-fold covers : {189,2,2}*1512, {63,2,6}*1512, {63,6,2}*1512, {21,2,18}*1512, {21,6,6}*1512a, {21,6,2}*1512, {21,6,6}*1512b
   10-fold covers : {21,2,20}*1680, {105,2,4}*1680, {42,2,10}*1680, {42,10,2}*1680, {210,2,2}*1680
   11-fold covers : {21,2,22}*1848, {231,2,2}*1848
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
s2 := (22,23);;
s3 := (24,25);;
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, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(25)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21);
s1 := Sym(25)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20);
s2 := Sym(25)!(22,23);
s3 := Sym(25)!(24,25);
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, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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