Polytope of Type {2,2,18,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,18,10}*1440
if this polytope has a name.
Group : SmallGroup(1440,4583)
Rank : 5
Schlafli Type : {2,2,18,10}
Number of vertices, edges, etc : 2, 2, 18, 90, 10
Order of s₀s₁s₂s₃s₄ : 90
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,6,10}*480
   5-fold quotients : {2,2,18,2}*288
   9-fold quotients : {2,2,2,10}*160
   10-fold quotients : {2,2,9,2}*144
   15-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,2,3,2}*48
   45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(20,36)(21,35)(22,37)(23,39)(24,38)
(25,40)(26,42)(27,41)(28,43)(29,45)(30,44)(31,46)(32,48)(33,47)(34,49)(51,52)
(54,55)(57,58)(60,61)(63,64)(65,81)(66,80)(67,82)(68,84)(69,83)(70,85)(71,87)
(72,86)(73,88)(74,90)(75,89)(76,91)(77,93)(78,92)(79,94);;
s3 := ( 5,20)( 6,22)( 7,21)( 8,32)( 9,34)(10,33)(11,29)(12,31)(13,30)(14,26)
(15,28)(16,27)(17,23)(18,25)(19,24)(35,36)(38,48)(39,47)(40,49)(41,45)(42,44)
(43,46)(50,65)(51,67)(52,66)(53,77)(54,79)(55,78)(56,74)(57,76)(58,75)(59,71)
(60,73)(61,72)(62,68)(63,70)(64,69)(80,81)(83,93)(84,92)(85,94)(86,90)(87,89)
(88,91);;
s4 := ( 5,53)( 6,54)( 7,55)( 8,50)( 9,51)(10,52)(11,62)(12,63)(13,64)(14,59)
(15,60)(16,61)(17,56)(18,57)(19,58)(20,68)(21,69)(22,70)(23,65)(24,66)(25,67)
(26,77)(27,78)(28,79)(29,74)(30,75)(31,76)(32,71)(33,72)(34,73)(35,83)(36,84)
(37,85)(38,80)(39,81)(40,82)(41,92)(42,93)(43,94)(44,89)(45,90)(46,91)(47,86)
(48,87)(49,88);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(94)!(1,2);
s1 := Sym(94)!(3,4);
s2 := Sym(94)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(20,36)(21,35)(22,37)(23,39)
(24,38)(25,40)(26,42)(27,41)(28,43)(29,45)(30,44)(31,46)(32,48)(33,47)(34,49)
(51,52)(54,55)(57,58)(60,61)(63,64)(65,81)(66,80)(67,82)(68,84)(69,83)(70,85)
(71,87)(72,86)(73,88)(74,90)(75,89)(76,91)(77,93)(78,92)(79,94);
s3 := Sym(94)!( 5,20)( 6,22)( 7,21)( 8,32)( 9,34)(10,33)(11,29)(12,31)(13,30)
(14,26)(15,28)(16,27)(17,23)(18,25)(19,24)(35,36)(38,48)(39,47)(40,49)(41,45)
(42,44)(43,46)(50,65)(51,67)(52,66)(53,77)(54,79)(55,78)(56,74)(57,76)(58,75)
(59,71)(60,73)(61,72)(62,68)(63,70)(64,69)(80,81)(83,93)(84,92)(85,94)(86,90)
(87,89)(88,91);
s4 := Sym(94)!( 5,53)( 6,54)( 7,55)( 8,50)( 9,51)(10,52)(11,62)(12,63)(13,64)
(14,59)(15,60)(16,61)(17,56)(18,57)(19,58)(20,68)(21,69)(22,70)(23,65)(24,66)
(25,67)(26,77)(27,78)(28,79)(29,74)(30,75)(31,76)(32,71)(33,72)(34,73)(35,83)
(36,84)(37,85)(38,80)(39,81)(40,82)(41,92)(42,93)(43,94)(44,89)(45,90)(46,91)
(47,86)(48,87)(49,88);
poly := sub<Sym(94)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope