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Polytope of Type {23,2,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {23,2,2,2}*368
if this polytope has a name.
Group : SmallGroup(368,41)
Rank : 5
Schlafli Type : {23,2,2,2}
Number of vertices, edges, etc : 23, 23, 2, 2, 2
Order of s0s1s2s3s4 : 46
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {23,2,2,2,2} of size 736
   {23,2,2,2,3} of size 1104
   {23,2,2,2,4} of size 1472
   {23,2,2,2,5} of size 1840
Vertex Figure Of :
   {2,23,2,2,2} of size 736
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {23,2,2,4}*736, {23,2,4,2}*736, {46,2,2,2}*736
   3-fold covers : {23,2,2,6}*1104, {23,2,6,2}*1104, {69,2,2,2}*1104
   4-fold covers : {23,2,4,4}*1472, {23,2,2,8}*1472, {23,2,8,2}*1472, {46,2,2,4}*1472, {46,2,4,2}*1472, {46,4,2,2}*1472, {92,2,2,2}*1472
   5-fold covers : {23,2,2,10}*1840, {23,2,10,2}*1840, {115,2,2,2}*1840
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);;
s2 := (24,25);;
s3 := (26,27);;
s4 := (28,29);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(29)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23);
s1 := Sym(29)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22);
s2 := Sym(29)!(24,25);
s3 := Sym(29)!(26,27);
s4 := Sym(29)!(28,29);
poly := sub<Sym(29)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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*s0*s1*s0*s1 >; 
 

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