Polytope of Type {2,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,46}*184
if this polytope has a name.
Group : SmallGroup(184,11)
Rank : 3
Schlafli Type : {2,46}
Number of vertices, edges, etc : 2, 46, 46
Order of s₀s₁s₂ : 46
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,46,2} of size 368
   {2,46,4} of size 736
   {2,46,6} of size 1104
   {2,46,8} of size 1472
   {2,46,10} of size 1840
Vertex Figure Of :
   {2,2,46} of size 368
   {3,2,46} of size 552
   {4,2,46} of size 736
   {5,2,46} of size 920
   {6,2,46} of size 1104
   {7,2,46} of size 1288
   {8,2,46} of size 1472
   {9,2,46} of size 1656
   {10,2,46} of size 1840
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,23}*92
   23-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,92}*368, {4,46}*368
   3-fold covers : {6,46}*552, {2,138}*552
   4-fold covers : {4,92}*736, {2,184}*736, {8,46}*736
   5-fold covers : {10,46}*920, {2,230}*920
   6-fold covers : {12,46}*1104, {6,92}*1104a, {2,276}*1104, {4,138}*1104a
   7-fold covers : {14,46}*1288, {2,322}*1288
   8-fold covers : {8,92}*1472a, {4,184}*1472a, {8,92}*1472b, {4,184}*1472b, {4,92}*1472, {16,46}*1472, {2,368}*1472
   9-fold covers : {18,46}*1656, {2,414}*1656, {6,138}*1656a, {6,138}*1656b, {6,138}*1656c
   10-fold covers : {20,46}*1840, {10,92}*1840, {2,460}*1840, {4,230}*1840
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 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)(43,44)(45,46)
(47,48);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,27)(24,25)(26,31)(28,29)(30,35)(32,33)(34,39)(36,37)(38,43)(40,41)(42,47)
(44,45)(46,48);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(48)!(1,2);
s1 := Sym(48)!( 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)(43,44)
(45,46)(47,48);
s2 := Sym(48)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,27)(24,25)(26,31)(28,29)(30,35)(32,33)(34,39)(36,37)(38,43)(40,41)
(42,47)(44,45)(46,48);
poly := sub<Sym(48)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope