Polytope of Type {2,14,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,8}*448
if this polytope has a name.
Group : SmallGroup(448,1207)
Rank : 4
Schlafli Type : {2,14,8}
Number of vertices, edges, etc : 2, 14, 56, 8
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,8,2} of size 896
   {2,14,8,4} of size 1792
   {2,14,8,4} of size 1792
Vertex Figure Of :
   {2,2,14,8} of size 896
   {3,2,14,8} of size 1344
   {4,2,14,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,4}*224
   4-fold quotients : {2,14,2}*112
   7-fold quotients : {2,2,8}*64
   8-fold quotients : {2,7,2}*56
   14-fold quotients : {2,2,4}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,8}*896a, {4,14,8}*896, {2,14,16}*896
   3-fold covers : {2,14,24}*1344, {6,14,8}*1344, {2,42,8}*1344
   4-fold covers : {2,28,8}*1792a, {2,56,8}*1792a, {2,56,8}*1792c, {8,14,8}*1792, {4,28,8}*1792a, {2,28,16}*1792a, {2,28,16}*1792b, {4,14,16}*1792, {2,14,32}*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)(17,25)(18,24)(19,30)(20,29)
(21,28)(22,27)(23,26)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)(38,53)
(39,52)(40,58)(41,57)(42,56)(43,55)(44,54);;
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)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)
(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)(17,25)(18,24)(19,30)
(20,29)(21,28)(22,27)(23,26)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)
(38,53)(39,52)(40,58)(41,57)(42,56)(43,55)(44,54);
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)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)
(23,58)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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