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Polytope of Type {2,2,23}

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

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