Polytope of Type {4,46}

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

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

References : None.
to this polytope