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Polytope of Type {15,2,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,2,28}*1680
if this polytope has a name.
Group : SmallGroup(1680,717)
Rank : 4
Schlafli Type : {15,2,28}
Number of vertices, edges, etc : 15, 15, 28, 28
Order of s0s1s2s3 : 420
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 : {15,2,14}*840
   3-fold quotients : {5,2,28}*560
   4-fold quotients : {15,2,7}*420
   5-fold quotients : {3,2,28}*336
   6-fold quotients : {5,2,14}*280
   7-fold quotients : {15,2,4}*240
   10-fold quotients : {3,2,14}*168
   12-fold quotients : {5,2,7}*140
   14-fold quotients : {15,2,2}*120
   20-fold quotients : {3,2,7}*84
   21-fold quotients : {5,2,4}*80
   35-fold quotients : {3,2,4}*48
   42-fold quotients : {5,2,2}*40
   70-fold quotients : {3,2,2}*24
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);;
s2 := (17,18)(19,20)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,37)
(38,41)(39,40)(42,43);;
s3 := (16,22)(17,19)(18,28)(20,30)(21,24)(23,26)(25,36)(27,38)(29,32)(31,34)
(33,42)(35,39)(37,40)(41,43);;
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, 
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(43)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(43)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s2 := Sym(43)!(17,18)(19,20)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)
(36,37)(38,41)(39,40)(42,43);
s3 := Sym(43)!(16,22)(17,19)(18,28)(20,30)(21,24)(23,26)(25,36)(27,38)(29,32)
(31,34)(33,42)(35,39)(37,40)(41,43);
poly := sub<Sym(43)|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, 
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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