Polytope of Type {2,41}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,41}*164
if this polytope has a name.
Group : SmallGroup(164,4)
Rank : 3
Schlafli Type : {2,41}
Number of vertices, edges, etc : 2, 41, 41
Order of s₀s₁s₂ : 82
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,41,2} of size 328
Vertex Figure Of :
   {2,2,41} of size 328
   {3,2,41} of size 492
   {4,2,41} of size 656
   {5,2,41} of size 820
   {6,2,41} of size 984
   {7,2,41} of size 1148
   {8,2,41} of size 1312
   {9,2,41} of size 1476
   {10,2,41} of size 1640
   {11,2,41} of size 1804
   {12,2,41} of size 1968
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,82}*328
   3-fold covers : {2,123}*492
   4-fold covers : {2,164}*656, {4,82}*656
   5-fold covers : {2,205}*820
   6-fold covers : {6,82}*984, {2,246}*984
   7-fold covers : {2,287}*1148
   8-fold covers : {4,164}*1312, {8,82}*1312, {2,328}*1312
   9-fold covers : {2,369}*1476, {6,123}*1476
   10-fold covers : {10,82}*1640, {2,410}*1640
   11-fold covers : {2,451}*1804
   12-fold covers : {12,82}*1968, {6,164}*1968a, {2,492}*1968, {4,246}*1968a, {6,123}*1968, {4,123}*1968
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)(34,35)(36,37)(38,39)(40,41)(42,43);;
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)(35,36)(37,38)(39,40)(41,42);;
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*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(43)!(1,2);
s1 := Sym(43)!( 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)(34,35)(36,37)(38,39)(40,41)(42,43);
s2 := Sym(43)!( 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)(35,36)(37,38)(39,40)(41,42);
poly := sub<Sym(43)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope