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Polytope of Type {64}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {64}*128
Also Known As : 64-gon, {64}. if this polytope has another name.
Group : SmallGroup(128,161)
Rank : 2
Schlafli Type : {64}
Number of vertices, edges, etc : 64, 64
Order of s0s1 : 64
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {64,2} of size 256
   {64,4} of size 512
   {64,4} of size 512
   {64,6} of size 768
   {64,10} of size 1280
   {64,14} of size 1792
Vertex Figure Of :
   {2,64} of size 256
   {4,64} of size 512
   {4,64} of size 512
   {6,64} of size 768
   {10,64} of size 1280
   {14,64} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {32}*64
   4-fold quotients : {16}*32
   8-fold quotients : {8}*16
   16-fold quotients : {4}*8
   32-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {128}*256
   3-fold covers : {192}*384
   4-fold covers : {256}*512
   5-fold covers : {320}*640
   6-fold covers : {384}*768
   7-fold covers : {448}*896
   9-fold covers : {576}*1152
   10-fold covers : {640}*1280
   11-fold covers : {704}*1408
   13-fold covers : {832}*1664
   14-fold covers : {896}*1792
   15-fold covers : {960}*1920
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);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(64)!( 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(64)!( 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);
poly := sub<Sym(64)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*s0*s1 >; 
 
References : None.
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