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Polytope of Type {2,8,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,14}*448
if this polytope has a name.
Group : SmallGroup(448,1207)
Rank : 4
Schlafli Type : {2,8,14}
Number of vertices, edges, etc : 2, 8, 56, 14
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,14,2} of size 896
   {2,8,14,4} of size 1792
Vertex Figure Of :
   {2,2,8,14} of size 896
   {3,2,8,14} of size 1344
   {4,2,8,14} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,14}*224
   4-fold quotients : {2,2,14}*112
   7-fold quotients : {2,8,2}*64
   8-fold quotients : {2,2,7}*56
   14-fold quotients : {2,4,2}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,28}*896a, {4,8,14}*896a, {2,16,14}*896
   3-fold covers : {2,24,14}*1344, {6,8,14}*1344, {2,8,42}*1344
   4-fold covers : {4,8,14}*1792a, {2,8,28}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {2,8,56}*1792a, {2,8,56}*1792c, {4,8,28}*1792d, {4,16,14}*1792a, {2,16,28}*1792a, {4,16,14}*1792b, {2,16,28}*1792b, {2,32,14}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (17,24)(18,25)(19,26)(20,27)(21,28)(22,29)(23,30)(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);;
s2 := ( 3,31)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,38)(11,44)(12,43)
(13,42)(14,41)(15,40)(16,39)(17,52)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)
(24,45)(25,51)(26,50)(27,49)(28,48)(29,47)(30,46);;
s3 := ( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)(24,25)
(26,30)(27,29)(31,32)(33,37)(34,36)(38,39)(40,44)(41,43)(45,46)(47,51)(48,50)
(52,53)(54,58)(55,57);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(58)!(1,2);
s1 := Sym(58)!(17,24)(18,25)(19,26)(20,27)(21,28)(22,29)(23,30)(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);
s2 := Sym(58)!( 3,31)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,38)(11,44)
(12,43)(13,42)(14,41)(15,40)(16,39)(17,52)(18,58)(19,57)(20,56)(21,55)(22,54)
(23,53)(24,45)(25,51)(26,50)(27,49)(28,48)(29,47)(30,46);
s3 := 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)(31,32)(33,37)(34,36)(38,39)(40,44)(41,43)(45,46)(47,51)
(48,50)(52,53)(54,58)(55,57);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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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