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Polytope of Type {8,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,18}*576
if this polytope has a name.
Group : SmallGroup(576,1738)
Rank : 4
Schlafli Type : {8,2,18}
Number of vertices, edges, etc : 8, 8, 18, 18
Order of s0s1s2s3 : 72
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,18,2} of size 1152
Vertex Figure Of :
   {2,8,2,18} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,2,9}*288, {4,2,18}*288
   3-fold quotients : {8,2,6}*192
   4-fold quotients : {4,2,9}*144, {2,2,18}*144
   6-fold quotients : {8,2,3}*96, {4,2,6}*96
   8-fold quotients : {2,2,9}*72
   9-fold quotients : {8,2,2}*64
   12-fold quotients : {4,2,3}*48, {2,2,6}*48
   18-fold quotients : {4,2,2}*32
   24-fold quotients : {2,2,3}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,18}*1152a, {8,2,36}*1152, {16,2,18}*1152
   3-fold covers : {8,2,54}*1728, {24,2,18}*1728, {8,6,18}*1728a, {8,6,18}*1728b
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
s3 := ( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,26);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(26)!(2,3)(4,5)(6,7);
s1 := Sym(26)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(26)!(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
s3 := Sym(26)!( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,26);
poly := sub<Sym(26)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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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