Polytope of Type {8,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,14,2}*448
if this polytope has a name.
Group : SmallGroup(448,1207)
Rank : 4
Schlafli Type : {8,14,2}
Number of vertices, edges, etc : 8, 56, 14, 2
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,14,2,2} of size 896
   {8,14,2,3} of size 1344
   {8,14,2,4} of size 1792
Vertex Figure Of :
   {2,8,14,2} of size 896
   {4,8,14,2} of size 1792
   {4,8,14,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,14,2}*224
   4-fold quotients : {2,14,2}*112
   7-fold quotients : {8,2,2}*64
   8-fold quotients : {2,7,2}*56
   14-fold quotients : {4,2,2}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,28,2}*896a, {8,14,4}*896, {16,14,2}*896
   3-fold covers : {24,14,2}*1344, {8,14,6}*1344, {8,42,2}*1344
   4-fold covers : {8,28,2}*1792a, {8,56,2}*1792a, {8,56,2}*1792c, {8,14,8}*1792, {8,28,4}*1792a, {16,28,2}*1792a, {16,28,2}*1792b, {16,14,4}*1792, {32,14,2}*1792
Permutation Representation (GAP) :

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