Polytope of Type {2,14,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,4,4}*896
if this polytope has a name.
Group : SmallGroup(896,17749)
Rank : 5
Schlafli Type : {2,14,4,4}
Number of vertices, edges, etc : 2, 14, 28, 8, 4
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,4,4,2} of size 1792
Vertex Figure Of :
   {2,2,14,4,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,2,4}*448, {2,14,4,2}*448
   4-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
   7-fold quotients : {2,2,4,4}*128
   8-fold quotients : {2,7,2,2}*112
   14-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   28-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,4,4}*1792, {4,14,4,4}*1792, {2,14,4,8}*1792a, {2,14,8,4}*1792a, {2,14,4,8}*1792b, {2,14,8,4}*1792b, {2,14,4,4}*1792
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)
(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)
(53,58)(54,57)(55,56);;
s2 := ( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)(24,25)
(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,53)(46,52)
(47,58)(48,57)(49,56)(50,55)(51,54);;
s3 := ( 3,31)( 4,32)( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)
(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)
(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58);;
s4 := (31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)
(41,55)(42,56)(43,57)(44,58);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(58)!(1,2);
s1 := Sym(58)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)
(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)
(48,49)(53,58)(54,57)(55,56);
s2 := Sym(58)!( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)
(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,53)
(46,52)(47,58)(48,57)(49,56)(50,55)(51,54);
s3 := Sym(58)!( 3,31)( 4,32)( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)
(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)
(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58);
s4 := Sym(58)!(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)
(40,54)(41,55)(42,56)(43,57)(44,58);
poly := sub<Sym(58)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope