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Polytope of Type {16,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,2,30}*1920
if this polytope has a name.
Group : SmallGroup(1920,203894)
Rank : 4
Schlafli Type : {16,2,30}
Number of vertices, edges, etc : 16, 16, 30, 30
Order of s0s1s2s3 : 240
Order of s0s1s2s3s2s1 : 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 : {16,2,15}*960, {8,2,30}*960
   3-fold quotients : {16,2,10}*640
   4-fold quotients : {8,2,15}*480, {4,2,30}*480
   5-fold quotients : {16,2,6}*384
   6-fold quotients : {16,2,5}*320, {8,2,10}*320
   8-fold quotients : {4,2,15}*240, {2,2,30}*240
   10-fold quotients : {16,2,3}*192, {8,2,6}*192
   12-fold quotients : {8,2,5}*160, {4,2,10}*160
   15-fold quotients : {16,2,2}*128
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {8,2,3}*96, {4,2,6}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {8,2,2}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {4,2,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := (19,20)(21,22)(23,24)(25,26)(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)
(39,42)(40,41)(43,46)(44,45);;
s3 := (17,33)(18,27)(19,25)(20,35)(21,23)(22,43)(24,29)(26,39)(28,37)(30,45)
(31,34)(32,44)(36,41)(38,40)(42,46);;
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*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*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(46)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(46)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(46)!(19,20)(21,22)(23,24)(25,26)(27,30)(28,29)(31,32)(33,36)(34,35)
(37,38)(39,42)(40,41)(43,46)(44,45);
s3 := Sym(46)!(17,33)(18,27)(19,25)(20,35)(21,23)(22,43)(24,29)(26,39)(28,37)
(30,45)(31,34)(32,44)(36,41)(38,40)(42,46);
poly := sub<Sym(46)|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*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*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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