Polytope of Type {46,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,4}*368
Also Known As : {46,4|2}. if this polytope has another name.
Group : SmallGroup(368,31)
Rank : 3
Schlafli Type : {46,4}
Number of vertices, edges, etc : 46, 92, 4
Order of s₀s₁s₂ : 92
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {46,4,2} of size 736
   {46,4,4} of size 1472
Vertex Figure Of :
   {2,46,4} of size 736
   {4,46,4} of size 1472
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {46,2}*184
   4-fold quotients : {23,2}*92
   23-fold quotients : {2,4}*16
   46-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {92,4}*736, {46,8}*736
   3-fold covers : {46,12}*1104, {138,4}*1104a
   4-fold covers : {92,8}*1472a, {184,4}*1472a, {92,8}*1472b, {184,4}*1472b, {92,4}*1472, {46,16}*1472
   5-fold covers : {46,20}*1840, {230,4}*1840
Permutation Representation (GAP) :

s0 := ( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)
(12,13)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)
(35,36)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)
(58,59)(71,92)(72,91)(73,90)(74,89)(75,88)(76,87)(77,86)(78,85)(79,84)(80,83)
(81,82);;
s1 := ( 1, 2)( 3,23)( 4,22)( 5,21)( 6,20)( 7,19)( 8,18)( 9,17)(10,16)(11,15)
(12,14)(24,25)(26,46)(27,45)(28,44)(29,43)(30,42)(31,41)(32,40)(33,39)(34,38)
(35,37)(47,71)(48,70)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)
(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)
(68,73)(69,72);;
s2 := ( 1,47)( 2,48)( 3,49)( 4,50)( 5,51)( 6,52)( 7,53)( 8,54)( 9,55)(10,56)
(11,57)(12,58)(13,59)(14,60)(15,61)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)
(22,68)(23,69)(24,70)(25,71)(26,72)(27,73)(28,74)(29,75)(30,76)(31,77)(32,78)
(33,79)(34,80)(35,81)(36,82)(37,83)(38,84)(39,85)(40,86)(41,87)(42,88)(43,89)
(44,90)(45,91)(46,92);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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(92)!( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)
(11,14)(12,13)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)
(34,37)(35,36)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)
(57,60)(58,59)(71,92)(72,91)(73,90)(74,89)(75,88)(76,87)(77,86)(78,85)(79,84)
(80,83)(81,82);
s1 := Sym(92)!( 1, 2)( 3,23)( 4,22)( 5,21)( 6,20)( 7,19)( 8,18)( 9,17)(10,16)
(11,15)(12,14)(24,25)(26,46)(27,45)(28,44)(29,43)(30,42)(31,41)(32,40)(33,39)
(34,38)(35,37)(47,71)(48,70)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)
(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)
(67,74)(68,73)(69,72);
s2 := Sym(92)!( 1,47)( 2,48)( 3,49)( 4,50)( 5,51)( 6,52)( 7,53)( 8,54)( 9,55)
(10,56)(11,57)(12,58)(13,59)(14,60)(15,61)(16,62)(17,63)(18,64)(19,65)(20,66)
(21,67)(22,68)(23,69)(24,70)(25,71)(26,72)(27,73)(28,74)(29,75)(30,76)(31,77)
(32,78)(33,79)(34,80)(35,81)(36,82)(37,83)(38,84)(39,85)(40,86)(41,87)(42,88)
(43,89)(44,90)(45,91)(46,92);
poly := sub<Sym(92)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 >;

References : None.
to this polytope