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Polytope of Type {64,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {64,2}*256
if this polytope has a name.
Group : SmallGroup(256,6726)
Rank : 3
Schlafli Type : {64,2}
Number of vertices, edges, etc : 64, 64, 2
Order of s0s1s2 : 64
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {64,2,2} of size 512
   {64,2,3} of size 768
   {64,2,5} of size 1280
   {64,2,7} of size 1792
Vertex Figure Of :
   {2,64,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {32,2}*128
   4-fold quotients : {16,2}*64
   8-fold quotients : {8,2}*32
   16-fold quotients : {4,2}*16
   32-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {64,4}*512a, {128,2}*512
   3-fold covers : {64,6}*768, {192,2}*768
   5-fold covers : {64,10}*1280, {320,2}*1280
   7-fold covers : {64,14}*1792, {448,2}*1792
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9,13)(10,14)(11,16)(12,15)(17,25)(18,26)(19,28)
(20,27)(21,31)(22,32)(23,29)(24,30)(33,49)(34,50)(35,52)(36,51)(37,55)(38,56)
(39,53)(40,54)(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);;
s1 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,45)(10,46)
(11,48)(12,47)(13,41)(14,42)(15,44)(16,43)(17,57)(18,58)(19,60)(20,59)(21,63)
(22,64)(23,61)(24,62)(25,49)(26,50)(27,52)(28,51)(29,55)(30,56)(31,53)
(32,54);;
s2 := (65,66);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(66)!( 3, 4)( 5, 7)( 6, 8)( 9,13)(10,14)(11,16)(12,15)(17,25)(18,26)
(19,28)(20,27)(21,31)(22,32)(23,29)(24,30)(33,49)(34,50)(35,52)(36,51)(37,55)
(38,56)(39,53)(40,54)(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);
s1 := Sym(66)!( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,45)
(10,46)(11,48)(12,47)(13,41)(14,42)(15,44)(16,43)(17,57)(18,58)(19,60)(20,59)
(21,63)(22,64)(23,61)(24,62)(25,49)(26,50)(27,52)(28,51)(29,55)(30,56)(31,53)
(32,54);
s2 := Sym(66)!(65,66);
poly := sub<Sym(66)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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