Polytope of Type {14,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,30}*1680
if this polytope has a name.
Group : SmallGroup(1680,988)
Rank : 4
Schlafli Type : {14,2,30}
Number of vertices, edges, etc : 14, 14, 30, 30
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 : {7,2,30}*840, {14,2,15}*840
   3-fold quotients : {14,2,10}*560
   4-fold quotients : {7,2,15}*420
   5-fold quotients : {14,2,6}*336
   6-fold quotients : {7,2,10}*280, {14,2,5}*280
   7-fold quotients : {2,2,30}*240
   10-fold quotients : {7,2,6}*168, {14,2,3}*168
   12-fold quotients : {7,2,5}*140
   14-fold quotients : {2,2,15}*120
   15-fold quotients : {14,2,2}*112
   20-fold quotients : {7,2,3}*84
   21-fold quotients : {2,2,10}*80
   30-fold quotients : {7,2,2}*56
   35-fold quotients : {2,2,6}*48
   42-fold quotients : {2,2,5}*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)(11,12)(13,14);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);;
s2 := (17,18)(19,20)(21,22)(23,24)(25,28)(26,27)(29,30)(31,34)(32,33)(35,36)
(37,40)(38,39)(41,44)(42,43);;
s3 := (15,31)(16,25)(17,23)(18,33)(19,21)(20,41)(22,27)(24,37)(26,35)(28,43)
(29,32)(30,42)(34,39)(36,38)(40,44);;
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, 
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(44)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(44)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
s2 := Sym(44)!(17,18)(19,20)(21,22)(23,24)(25,28)(26,27)(29,30)(31,34)(32,33)
(35,36)(37,40)(38,39)(41,44)(42,43);
s3 := Sym(44)!(15,31)(16,25)(17,23)(18,33)(19,21)(20,41)(22,27)(24,37)(26,35)
(28,43)(29,32)(30,42)(34,39)(36,38)(40,44);
poly := sub<Sym(44)|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, 
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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