Polytope of Type {4,2,14,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,14,8}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044755)
Rank : 5
Schlafli Type : {4,2,14,8}
Number of vertices, edges, etc : 4, 4, 14, 56, 8
Order of s₀s₁s₂s₃s₄ : 56
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {4,2,14,4}*896, {2,2,14,8}*896
   4-fold quotients : {2,2,14,4}*448, {4,2,14,2}*448
   7-fold quotients : {4,2,2,8}*256
   8-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
   14-fold quotients : {4,2,2,4}*128, {2,2,2,8}*128
   16-fold quotients : {2,2,7,2}*112
   28-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)
(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)
(55,60)(56,59)(57,58);;
s3 := ( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,27)(20,26)(21,32)(22,31)
(23,30)(24,29)(25,28)(33,48)(34,47)(35,53)(36,52)(37,51)(38,50)(39,49)(40,55)
(41,54)(42,60)(43,59)(44,58)(45,57)(46,56);;
s4 := ( 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)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)(25,60)
(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(60)!(2,3);
s1 := Sym(60)!(1,2)(3,4);
s2 := Sym(60)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)
(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)
(50,51)(55,60)(56,59)(57,58);
s3 := Sym(60)!( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,27)(20,26)(21,32)
(22,31)(23,30)(24,29)(25,28)(33,48)(34,47)(35,53)(36,52)(37,51)(38,50)(39,49)
(40,55)(41,54)(42,60)(43,59)(44,58)(45,57)(46,56);
s4 := Sym(60)!( 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)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)
(25,60)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53);
poly := sub<Sym(60)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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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