Polytope of Type {2,2,30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,30,6}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5949)
Rank : 5
Schlafli Type : {2,2,30,6}
Number of vertices, edges, etc : 2, 2, 30, 90, 6
Order of s₀s₁s₂s₃s₄ : 30
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) :
   2-fold quotients : {2,2,15,6}*720
   3-fold quotients : {2,2,30,2}*480
   5-fold quotients : {2,2,6,6}*288c
   6-fold quotients : {2,2,15,2}*240
   9-fold quotients : {2,2,10,2}*160
   10-fold quotients : {2,2,3,6}*144
   15-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,5,2}*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, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)
(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)
(34,41)(51,54)(52,53)(55,60)(56,64)(57,63)(58,62)(59,61)(65,80)(66,84)(67,83)
(68,82)(69,81)(70,90)(71,94)(72,93)(73,92)(74,91)(75,85)(76,89)(77,88)(78,87)
(79,86);;
s3 := ( 5,71)( 6,70)( 7,74)( 8,73)( 9,72)(10,66)(11,65)(12,69)(13,68)(14,67)
(15,76)(16,75)(17,79)(18,78)(19,77)(20,56)(21,55)(22,59)(23,58)(24,57)(25,51)
(26,50)(27,54)(28,53)(29,52)(30,61)(31,60)(32,64)(33,63)(34,62)(35,86)(36,85)
(37,89)(38,88)(39,87)(40,81)(41,80)(42,84)(43,83)(44,82)(45,91)(46,90)(47,94)
(48,93)(49,92);;
s4 := (20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)
(30,45)(31,46)(32,47)(33,48)(34,49)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)
(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92)(78,93)(79,94);;
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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*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*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*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, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)
(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)
(33,42)(34,41)(51,54)(52,53)(55,60)(56,64)(57,63)(58,62)(59,61)(65,80)(66,84)
(67,83)(68,82)(69,81)(70,90)(71,94)(72,93)(73,92)(74,91)(75,85)(76,89)(77,88)
(78,87)(79,86);
s3 := Sym(94)!( 5,71)( 6,70)( 7,74)( 8,73)( 9,72)(10,66)(11,65)(12,69)(13,68)
(14,67)(15,76)(16,75)(17,79)(18,78)(19,77)(20,56)(21,55)(22,59)(23,58)(24,57)
(25,51)(26,50)(27,54)(28,53)(29,52)(30,61)(31,60)(32,64)(33,63)(34,62)(35,86)
(36,85)(37,89)(38,88)(39,87)(40,81)(41,80)(42,84)(43,83)(44,82)(45,91)(46,90)
(47,94)(48,93)(49,92);
s4 := Sym(94)!(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)
(29,44)(30,45)(31,46)(32,47)(33,48)(34,49)(65,80)(66,81)(67,82)(68,83)(69,84)
(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92)(78,93)(79,94);
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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*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*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*s2*s3*s2*s3*s2*s3 >;

to this polytope