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Polytope of Type {46,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,2}*184
if this polytope has a name.
Group : SmallGroup(184,11)
Rank : 3
Schlafli Type : {46,2}
Number of vertices, edges, etc : 46, 46, 2
Order of s0s1s2 : 46
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 :
   {46,2,2} of size 368
   {46,2,3} of size 552
   {46,2,4} of size 736
   {46,2,5} of size 920
   {46,2,6} of size 1104
   {46,2,7} of size 1288
   {46,2,8} of size 1472
   {46,2,9} of size 1656
   {46,2,10} of size 1840
Vertex Figure Of :
   {2,46,2} of size 368
   {4,46,2} of size 736
   {6,46,2} of size 1104
   {8,46,2} of size 1472
   {10,46,2} of size 1840
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {23,2}*92
   23-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {92,2}*368, {46,4}*368
   3-fold covers : {46,6}*552, {138,2}*552
   4-fold covers : {92,4}*736, {184,2}*736, {46,8}*736
   5-fold covers : {46,10}*920, {230,2}*920
   6-fold covers : {46,12}*1104, {92,6}*1104a, {276,2}*1104, {138,4}*1104a
   7-fold covers : {46,14}*1288, {322,2}*1288
   8-fold covers : {92,8}*1472a, {184,4}*1472a, {92,8}*1472b, {184,4}*1472b, {92,4}*1472, {46,16}*1472, {368,2}*1472
   9-fold covers : {46,18}*1656, {414,2}*1656, {138,6}*1656a, {138,6}*1656b, {138,6}*1656c
   10-fold covers : {46,20}*1840, {92,10}*1840, {460,2}*1840, {230,4}*1840
Permutation Representation (GAP) :
s0 := ( 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)(43,44)
(45,46);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,45)
(42,43)(44,46);;
s2 := (47,48);;
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*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*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(48)!( 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)
(43,44)(45,46);
s1 := Sym(48)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)
(40,45)(42,43)(44,46);
s2 := Sym(48)!(47,48);
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*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*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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