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Polytope of Type {2,64}

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

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