Polytope of Type {2,30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,6}*720c
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 4
Schlafli Type : {2,30,6}
Number of vertices, edges, etc : 2, 30, 90, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,30,6,2} of size 1440
Vertex Figure Of :
   {2,2,30,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,15,6}*360
   3-fold quotients : {2,30,2}*240
   5-fold quotients : {2,6,6}*144c
   6-fold quotients : {2,15,2}*120
   9-fold quotients : {2,10,2}*80
   10-fold quotients : {2,3,6}*72
   15-fold quotients : {2,6,2}*48
   18-fold quotients : {2,5,2}*40
   30-fold quotients : {2,3,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,60,6}*1440c, {4,30,6}*1440c, {2,30,12}*1440c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope