Polytope of Type {2,18,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,10}*720
if this polytope has a name.
Group : SmallGroup(720,402)
Rank : 4
Schlafli Type : {2,18,10}
Number of vertices, edges, etc : 2, 18, 90, 10
Order of s₀s₁s₂s₃ : 90
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,18,10,2} of size 1440
Vertex Figure Of :
   {2,2,18,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,10}*240
   5-fold quotients : {2,18,2}*144
   9-fold quotients : {2,2,10}*80
   10-fold quotients : {2,9,2}*72
   15-fold quotients : {2,6,2}*48
   18-fold quotients : {2,2,5}*40
   30-fold quotients : {2,3,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,36,10}*1440, {2,18,20}*1440a, {4,18,10}*1440a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,34)(19,33)(20,35)(21,37)(22,36)
(23,38)(24,40)(25,39)(26,41)(27,43)(28,42)(29,44)(30,46)(31,45)(32,47)(49,50)
(52,53)(55,56)(58,59)(61,62)(63,79)(64,78)(65,80)(66,82)(67,81)(68,83)(69,85)
(70,84)(71,86)(72,88)(73,87)(74,89)(75,91)(76,90)(77,92);;
s2 := ( 3,18)( 4,20)( 5,19)( 6,30)( 7,32)( 8,31)( 9,27)(10,29)(11,28)(12,24)
(13,26)(14,25)(15,21)(16,23)(17,22)(33,34)(36,46)(37,45)(38,47)(39,43)(40,42)
(41,44)(48,63)(49,65)(50,64)(51,75)(52,77)(53,76)(54,72)(55,74)(56,73)(57,69)
(58,71)(59,70)(60,66)(61,68)(62,67)(78,79)(81,91)(82,90)(83,92)(84,88)(85,87)
(86,89);;
s3 := ( 3,51)( 4,52)( 5,53)( 6,48)( 7,49)( 8,50)( 9,60)(10,61)(11,62)(12,57)
(13,58)(14,59)(15,54)(16,55)(17,56)(18,66)(19,67)(20,68)(21,63)(22,64)(23,65)
(24,75)(25,76)(26,77)(27,72)(28,73)(29,74)(30,69)(31,70)(32,71)(33,81)(34,82)
(35,83)(36,78)(37,79)(38,80)(39,90)(40,91)(41,92)(42,87)(43,88)(44,89)(45,84)
(46,85)(47,86);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(1,2);
s1 := Sym(92)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,34)(19,33)(20,35)(21,37)
(22,36)(23,38)(24,40)(25,39)(26,41)(27,43)(28,42)(29,44)(30,46)(31,45)(32,47)
(49,50)(52,53)(55,56)(58,59)(61,62)(63,79)(64,78)(65,80)(66,82)(67,81)(68,83)
(69,85)(70,84)(71,86)(72,88)(73,87)(74,89)(75,91)(76,90)(77,92);
s2 := Sym(92)!( 3,18)( 4,20)( 5,19)( 6,30)( 7,32)( 8,31)( 9,27)(10,29)(11,28)
(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)(33,34)(36,46)(37,45)(38,47)(39,43)
(40,42)(41,44)(48,63)(49,65)(50,64)(51,75)(52,77)(53,76)(54,72)(55,74)(56,73)
(57,69)(58,71)(59,70)(60,66)(61,68)(62,67)(78,79)(81,91)(82,90)(83,92)(84,88)
(85,87)(86,89);
s3 := Sym(92)!( 3,51)( 4,52)( 5,53)( 6,48)( 7,49)( 8,50)( 9,60)(10,61)(11,62)
(12,57)(13,58)(14,59)(15,54)(16,55)(17,56)(18,66)(19,67)(20,68)(21,63)(22,64)
(23,65)(24,75)(25,76)(26,77)(27,72)(28,73)(29,74)(30,69)(31,70)(32,71)(33,81)
(34,82)(35,83)(36,78)(37,79)(38,80)(39,90)(40,91)(41,92)(42,87)(43,88)(44,89)
(45,84)(46,85)(47,86);
poly := sub<Sym(92)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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