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Polytope of Type {2,23,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,23,2}*184
if this polytope has a name.
Group : SmallGroup(184,11)
Rank : 4
Schlafli Type : {2,23,2}
Number of vertices, edges, etc : 2, 23, 23, 2
Order of s0s1s2s3 : 46
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,23,2,2} of size 368
   {2,23,2,3} of size 552
   {2,23,2,4} of size 736
   {2,23,2,5} of size 920
   {2,23,2,6} of size 1104
   {2,23,2,7} of size 1288
   {2,23,2,8} of size 1472
   {2,23,2,9} of size 1656
   {2,23,2,10} of size 1840
Vertex Figure Of :
   {2,2,23,2} of size 368
   {3,2,23,2} of size 552
   {4,2,23,2} of size 736
   {5,2,23,2} of size 920
   {6,2,23,2} of size 1104
   {7,2,23,2} of size 1288
   {8,2,23,2} of size 1472
   {9,2,23,2} of size 1656
   {10,2,23,2} of size 1840
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,46,2}*368
   3-fold covers : {2,69,2}*552
   4-fold covers : {2,92,2}*736, {2,46,4}*736, {4,46,2}*736
   5-fold covers : {2,115,2}*920
   6-fold covers : {2,46,6}*1104, {6,46,2}*1104, {2,138,2}*1104
   7-fold covers : {2,161,2}*1288
   8-fold covers : {2,92,4}*1472, {4,92,2}*1472, {4,46,4}*1472, {2,46,8}*1472, {8,46,2}*1472, {2,184,2}*1472
   9-fold covers : {2,207,2}*1656, {2,69,6}*1656, {6,69,2}*1656
   10-fold covers : {2,46,10}*1840, {10,46,2}*1840, {2,230,2}*1840
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24);;
s3 := (26,27);;
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, 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*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(27)!(1,2);
s1 := Sym(27)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25);
s2 := Sym(27)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24);
s3 := Sym(27)!(26,27);
poly := sub<Sym(27)|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, 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*s1*s2 >; 
 

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