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

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