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Polytope of Type {32,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,2}*128
if this polytope has a name.
Group : SmallGroup(128,991)
Rank : 3
Schlafli Type : {32,2}
Number of vertices, edges, etc : 32, 32, 2
Order of s0s1s2 : 32
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 :
   {32,2,2} of size 256
   {32,2,3} of size 384
   {32,2,5} of size 640
   {32,2,6} of size 768
   {32,2,7} of size 896
   {32,2,9} of size 1152
   {32,2,10} of size 1280
   {32,2,11} of size 1408
   {32,2,13} of size 1664
   {32,2,14} of size 1792
   {32,2,15} of size 1920
Vertex Figure Of :
   {2,32,2} of size 256
   {4,32,2} of size 512
   {4,32,2} of size 512
   {6,32,2} of size 768
   {10,32,2} of size 1280
   {14,32,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {16,2}*64
   4-fold quotients : {8,2}*32
   8-fold quotients : {4,2}*16
   16-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {32,4}*256a, {64,2}*256
   3-fold covers : {96,2}*384, {32,6}*384
   4-fold covers : {32,4}*512a, {32,8}*512a, {32,8}*512b, {64,4}*512a, {64,4}*512b, {128,2}*512
   5-fold covers : {160,2}*640, {32,10}*640
   6-fold covers : {32,12}*768a, {96,4}*768a, {64,6}*768, {192,2}*768
   7-fold covers : {224,2}*896, {32,14}*896
   9-fold covers : {32,18}*1152, {288,2}*1152, {96,6}*1152a, {96,6}*1152b, {96,6}*1152c, {32,6}*1152
   10-fold covers : {32,20}*1280a, {160,4}*1280a, {64,10}*1280, {320,2}*1280
   11-fold covers : {32,22}*1408, {352,2}*1408
   13-fold covers : {32,26}*1664, {416,2}*1664
   14-fold covers : {32,28}*1792a, {224,4}*1792a, {64,14}*1792, {448,2}*1792
   15-fold covers : {32,30}*1920, {480,2}*1920, {96,10}*1920, {160,6}*1920
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);;
s2 := (33,34);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(34)!( 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(34)!( 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);
s2 := Sym(34)!(33,34);
poly := sub<Sym(34)|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 >; 
 

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