Polytope of Type {2,2,29}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,29}*232
if this polytope has a name.
Group : SmallGroup(232,13)
Rank : 4
Schlafli Type : {2,2,29}
Number of vertices, edges, etc : 2, 2, 29, 29
Order of s₀s₁s₂s₃ : 58
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,29,2} of size 464
Vertex Figure Of :
   {2,2,2,29} of size 464
   {3,2,2,29} of size 696
   {4,2,2,29} of size 928
   {5,2,2,29} of size 1160
   {6,2,2,29} of size 1392
   {7,2,2,29} of size 1624
   {8,2,2,29} of size 1856
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,29}*464, {2,2,58}*464
   3-fold covers : {6,2,29}*696, {2,2,87}*696
   4-fold covers : {8,2,29}*928, {2,2,116}*928, {2,4,58}*928, {4,2,58}*928
   5-fold covers : {10,2,29}*1160, {2,2,145}*1160
   6-fold covers : {12,2,29}*1392, {4,2,87}*1392, {2,6,58}*1392, {6,2,58}*1392, {2,2,174}*1392
   7-fold covers : {14,2,29}*1624, {2,2,203}*1624
   8-fold covers : {16,2,29}*1856, {4,4,58}*1856, {2,4,116}*1856, {4,2,116}*1856, {2,8,58}*1856, {8,2,58}*1856, {2,2,232}*1856
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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);;
s3 := ( 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,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(33)!(1,2);
s1 := Sym(33)!(3,4);
s2 := Sym(33)!( 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);
s3 := Sym(33)!( 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(33)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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