Polytope of Type {18,10,2}

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

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

to this polytope