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Polytope of Type {2,32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,32}*128
if this polytope has a name.
Group : SmallGroup(128,991)
Rank : 3
Schlafli Type : {2,32}
Number of vertices, edges, etc : 2, 32, 32
Order of s0s1s2 : 32
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,32,2} of size 256
   {2,32,4} of size 512
   {2,32,4} of size 512
   {2,32,6} of size 768
   {2,32,10} of size 1280
   {2,32,14} of size 1792
Vertex Figure Of :
   {2,2,32} of size 256
   {3,2,32} of size 384
   {5,2,32} of size 640
   {6,2,32} of size 768
   {7,2,32} of size 896
   {9,2,32} of size 1152
   {10,2,32} of size 1280
   {11,2,32} of size 1408
   {13,2,32} of size 1664
   {14,2,32} of size 1792
   {15,2,32} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,16}*64
   4-fold quotients : {2,8}*32
   8-fold quotients : {2,4}*16
   16-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,32}*256a, {2,64}*256
   3-fold covers : {2,96}*384, {6,32}*384
   4-fold covers : {4,32}*512a, {8,32}*512a, {8,32}*512b, {4,64}*512a, {4,64}*512b, {2,128}*512
   5-fold covers : {2,160}*640, {10,32}*640
   6-fold covers : {12,32}*768a, {4,96}*768a, {6,64}*768, {2,192}*768
   7-fold covers : {2,224}*896, {14,32}*896
   9-fold covers : {18,32}*1152, {2,288}*1152, {6,96}*1152a, {6,96}*1152b, {6,96}*1152c, {6,32}*1152
   10-fold covers : {20,32}*1280a, {4,160}*1280a, {10,64}*1280, {2,320}*1280
   11-fold covers : {22,32}*1408, {2,352}*1408
   13-fold covers : {26,32}*1664, {2,416}*1664
   14-fold covers : {28,32}*1792a, {4,224}*1792a, {14,64}*1792, {2,448}*1792
   15-fold covers : {30,32}*1920, {2,480}*1920, {10,96}*1920, {6,160}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)(32,33);;
s2 := ( 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)(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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(34)!(1,2);
s1 := Sym(34)!( 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)(32,33);
s2 := Sym(34)!( 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)(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*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 >; 
 

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