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Polytope of Type {32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32}*64
Also Known As : 32-gon, {32}. if this polytope has another name.
Group : SmallGroup(64,52)
Rank : 2
Schlafli Type : {32}
Number of vertices, edges, etc : 32, 32
Order of s0s1 : 32
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {32,2} of size 128
   {32,4} of size 256
   {32,4} of size 256
   {32,6} of size 384
   {32,4} of size 512
   {32,4} of size 512
   {32,8} of size 512
   {32,8} of size 512
   {32,8} of size 512
   {32,8} of size 512
   {32,10} of size 640
   {32,12} of size 768
   {32,12} of size 768
   {32,14} of size 896
   {32,18} of size 1152
   {32,6} of size 1152
   {32,20} of size 1280
   {32,20} of size 1280
   {32,22} of size 1408
   {32,26} of size 1664
   {32,28} of size 1792
   {32,28} of size 1792
   {32,30} of size 1920
Vertex Figure Of :
   {2,32} of size 128
   {4,32} of size 256
   {4,32} of size 256
   {6,32} of size 384
   {4,32} of size 512
   {4,32} of size 512
   {8,32} of size 512
   {8,32} of size 512
   {8,32} of size 512
   {8,32} of size 512
   {10,32} of size 640
   {12,32} of size 768
   {12,32} of size 768
   {14,32} of size 896
   {18,32} of size 1152
   {6,32} of size 1152
   {20,32} of size 1280
   {20,32} of size 1280
   {22,32} of size 1408
   {26,32} of size 1664
   {28,32} of size 1792
   {28,32} of size 1792
   {30,32} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {16}*32
   4-fold quotients : {8}*16
   8-fold quotients : {4}*8
   16-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {64}*128
   3-fold covers : {96}*192
   4-fold covers : {128}*256
   5-fold covers : {160}*320
   6-fold covers : {192}*384
   7-fold covers : {224}*448
   8-fold covers : {256}*512
   9-fold covers : {288}*576
   10-fold covers : {320}*640
   11-fold covers : {352}*704
   12-fold covers : {384}*768
   13-fold covers : {416}*832
   14-fold covers : {448}*896
   15-fold covers : {480}*960
   17-fold covers : {544}*1088
   18-fold covers : {576}*1152
   19-fold covers : {608}*1216
   20-fold covers : {640}*1280
   21-fold covers : {672}*1344
   22-fold covers : {704}*1408
   23-fold covers : {736}*1472
   25-fold covers : {800}*1600
   26-fold covers : {832}*1664
   27-fold covers : {864}*1728
   28-fold covers : {896}*1792
   29-fold covers : {928}*1856
   30-fold covers : {960}*1920
   31-fold covers : {992}*1984
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31);
s1 := Sym(32)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);
poly := sub<Sym(32)|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 >; 
 
References : None.
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