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Polytope of Type {10,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,42}*1680
if this polytope has a name.
Group : SmallGroup(1680,990)
Rank : 4
Schlafli Type : {10,2,42}
Number of vertices, edges, etc : 10, 10, 42, 42
Order of s0s1s2s3 : 210
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 : {5,2,42}*840, {10,2,21}*840
   3-fold quotients : {10,2,14}*560
   4-fold quotients : {5,2,21}*420
   5-fold quotients : {2,2,42}*336
   6-fold quotients : {5,2,14}*280, {10,2,7}*280
   7-fold quotients : {10,2,6}*240
   10-fold quotients : {2,2,21}*168
   12-fold quotients : {5,2,7}*140
   14-fold quotients : {5,2,6}*120, {10,2,3}*120
   15-fold quotients : {2,2,14}*112
   21-fold quotients : {10,2,2}*80
   28-fold quotients : {5,2,3}*60
   30-fold quotients : {2,2,7}*56
   35-fold quotients : {2,2,6}*48
   42-fold quotients : {5,2,2}*40
   70-fold quotients : {2,2,3}*24
   105-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (13,14)(15,16)(17,18)(19,20)(21,24)(22,23)(25,26)(27,30)(28,29)(31,32)
(33,36)(34,35)(37,38)(39,42)(40,41)(43,44)(45,48)(46,47)(49,52)(50,51);;
s3 := (11,27)(12,21)(13,19)(14,29)(15,17)(16,39)(18,23)(20,33)(22,31)(24,41)
(25,28)(26,49)(30,35)(32,45)(34,43)(36,51)(37,40)(38,50)(42,47)(44,46)
(48,52);;
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, 
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*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(52)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(52)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(52)!(13,14)(15,16)(17,18)(19,20)(21,24)(22,23)(25,26)(27,30)(28,29)
(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,44)(45,48)(46,47)(49,52)(50,51);
s3 := Sym(52)!(11,27)(12,21)(13,19)(14,29)(15,17)(16,39)(18,23)(20,33)(22,31)
(24,41)(25,28)(26,49)(30,35)(32,45)(34,43)(36,51)(37,40)(38,50)(42,47)(44,46)
(48,52);
poly := sub<Sym(52)|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, 
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*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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