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Polytope of Type {7,2,8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,8,8}*1792b
if this polytope has a name.
Group : SmallGroup(1792,145169)
Rank : 5
Schlafli Type : {7,2,8,8}
Number of vertices, edges, etc : 7, 7, 8, 32, 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 : {7,2,4,8}*896a, {7,2,8,4}*896a
   4-fold quotients : {7,2,4,4}*448, {7,2,2,8}*448, {7,2,8,2}*448
   8-fold quotients : {7,2,2,4}*224, {7,2,4,2}*224
   16-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 8,24)( 9,25)(10,26)(11,27)(12,29)(13,28)(14,31)(15,30)(16,33)(17,32)
(18,35)(19,34)(20,36)(21,37)(22,38)(23,39)(40,56)(41,57)(42,58)(43,59)(44,61)
(45,60)(46,63)(47,62)(48,65)(49,64)(50,67)(51,66)(52,68)(53,69)(54,70)
(55,71);;
s3 := (12,13)(14,15)(16,18)(17,19)(20,23)(21,22)(24,28)(25,29)(26,30)(27,31)
(32,38)(33,39)(34,36)(35,37)(40,48)(41,49)(42,50)(43,51)(44,53)(45,52)(46,55)
(47,54)(56,69)(57,68)(58,71)(59,70)(60,65)(61,64)(62,67)(63,66);;
s4 := ( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,67)(17,66)
(18,65)(19,64)(20,71)(21,70)(22,69)(23,68)(24,40)(25,41)(26,42)(27,43)(28,44)
(29,45)(30,46)(31,47)(32,51)(33,50)(34,49)(35,48)(36,55)(37,54)(38,53)
(39,52);;
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, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(71)!(2,3)(4,5)(6,7);
s1 := Sym(71)!(1,2)(3,4)(5,6);
s2 := Sym(71)!( 8,24)( 9,25)(10,26)(11,27)(12,29)(13,28)(14,31)(15,30)(16,33)
(17,32)(18,35)(19,34)(20,36)(21,37)(22,38)(23,39)(40,56)(41,57)(42,58)(43,59)
(44,61)(45,60)(46,63)(47,62)(48,65)(49,64)(50,67)(51,66)(52,68)(53,69)(54,70)
(55,71);
s3 := Sym(71)!(12,13)(14,15)(16,18)(17,19)(20,23)(21,22)(24,28)(25,29)(26,30)
(27,31)(32,38)(33,39)(34,36)(35,37)(40,48)(41,49)(42,50)(43,51)(44,53)(45,52)
(46,55)(47,54)(56,69)(57,68)(58,71)(59,70)(60,65)(61,64)(62,67)(63,66);
s4 := Sym(71)!( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,67)
(17,66)(18,65)(19,64)(20,71)(21,70)(22,69)(23,68)(24,40)(25,41)(26,42)(27,43)
(28,44)(29,45)(30,46)(31,47)(32,51)(33,50)(34,49)(35,48)(36,55)(37,54)(38,53)
(39,52);
poly := sub<Sym(71)|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, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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