Polytope of Type {14,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,24}*1344
if this polytope has a name.
Group : SmallGroup(1344,8472)
Rank : 4
Schlafli Type : {14,2,24}
Number of vertices, edges, etc : 14, 14, 24, 24
Order of s₀s₁s₂s₃ : 168
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 : {7,2,24}*672, {14,2,12}*672
   3-fold quotients : {14,2,8}*448
   4-fold quotients : {7,2,12}*336, {14,2,6}*336
   6-fold quotients : {7,2,8}*224, {14,2,4}*224
   7-fold quotients : {2,2,24}*192
   8-fold quotients : {7,2,6}*168, {14,2,3}*168
   12-fold quotients : {7,2,4}*112, {14,2,2}*112
   14-fold quotients : {2,2,12}*96
   16-fold quotients : {7,2,3}*84
   21-fold quotients : {2,2,8}*64
   24-fold quotients : {7,2,2}*56
   28-fold quotients : {2,2,6}*48
   42-fold quotients : {2,2,4}*32
   56-fold quotients : {2,2,3}*24
   84-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 := (16,17)(18,19)(20,23)(21,25)(22,24)(26,29)(27,31)(28,30)(33,36)(34,35)
(37,38);;
s3 := (15,21)(16,18)(17,27)(19,22)(20,24)(23,33)(25,28)(26,30)(29,37)(31,34)
(32,35)(36,38);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(38)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(38)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
s2 := Sym(38)!(16,17)(18,19)(20,23)(21,25)(22,24)(26,29)(27,31)(28,30)(33,36)
(34,35)(37,38);
s3 := Sym(38)!(15,21)(16,18)(17,27)(19,22)(20,24)(23,33)(25,28)(26,30)(29,37)
(31,34)(32,35)(36,38);
poly := sub<Sym(38)|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 >;

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