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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,18}*1440
if this polytope has a name.
Group : SmallGroup(1440,4583)
Rank : 5
Schlafli Type : {2,2,10,18}
Number of vertices, edges, etc : 2, 2, 10, 90, 18
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 : {2,2,10,6}*480
   5-fold quotients : {2,2,2,18}*288
   9-fold quotients : {2,2,10,2}*160
   10-fold quotients : {2,2,2,9}*144
   15-fold quotients : {2,2,2,6}*96
   18-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,2,3}*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 := ( 8,17)( 9,18)(10,19)(11,14)(12,15)(13,16)(23,32)(24,33)(25,34)(26,29)
(27,30)(28,31)(38,47)(39,48)(40,49)(41,44)(42,45)(43,46)(53,62)(54,63)(55,64)
(56,59)(57,60)(58,61)(68,77)(69,78)(70,79)(71,74)(72,75)(73,76)(83,92)(84,93)
(85,94)(86,89)(87,90)(88,91);;
s3 := ( 5, 8)( 6,10)( 7, 9)(11,17)(12,19)(13,18)(15,16)(20,39)(21,38)(22,40)
(23,36)(24,35)(25,37)(26,48)(27,47)(28,49)(29,45)(30,44)(31,46)(32,42)(33,41)
(34,43)(50,53)(51,55)(52,54)(56,62)(57,64)(58,63)(60,61)(65,84)(66,83)(67,85)
(68,81)(69,80)(70,82)(71,93)(72,92)(73,94)(74,90)(75,89)(76,91)(77,87)(78,86)
(79,88);;
s4 := ( 5,65)( 6,67)( 7,66)( 8,68)( 9,70)(10,69)(11,71)(12,73)(13,72)(14,74)
(15,76)(16,75)(17,77)(18,79)(19,78)(20,50)(21,52)(22,51)(23,53)(24,55)(25,54)
(26,56)(27,58)(28,57)(29,59)(30,61)(31,60)(32,62)(33,64)(34,63)(35,81)(36,80)
(37,82)(38,84)(39,83)(40,85)(41,87)(42,86)(43,88)(44,90)(45,89)(46,91)(47,93)
(48,92)(49,94);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope