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Polytope of Type {2,4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,136369)
Rank : 5
Schlafli Type : {2,4,6,4}
Number of vertices, edges, etc : 2, 12, 36, 36, 4
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,6,2}*576
   4-fold quotients : {2,4,6,2}*288
   9-fold quotients : {2,4,2,4}*128
   18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38);;
s2 := ( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(22,24)(23,27)(26,28)(31,33)
(32,36)(35,37);;
s3 := ( 3,22)( 4,21)( 5,23)( 6,28)( 7,27)( 8,29)( 9,25)(10,24)(11,26)(12,31)
(13,30)(14,32)(15,37)(16,36)(17,38)(18,34)(19,33)(20,35);;
s4 := (21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38);
s2 := Sym(38)!( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(22,24)(23,27)(26,28)
(31,33)(32,36)(35,37);
s3 := Sym(38)!( 3,22)( 4,21)( 5,23)( 6,28)( 7,27)( 8,29)( 9,25)(10,24)(11,26)
(12,31)(13,30)(14,32)(15,37)(16,36)(17,38)(18,34)(19,33)(20,35);
s4 := Sym(38)!(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);
poly := sub<Sym(38)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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