Polytope of Type {2,6,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,10}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {2,6,6,10}
Number of vertices, edges, etc : 2, 6, 18, 30, 10
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
   5-fold quotients : {2,6,6,2}*288b
   9-fold quotients : {2,2,2,10}*160
   10-fold quotients : {2,6,3,2}*144
   15-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,2,5}*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 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)
(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62)(68,73)
(69,74)(70,75)(71,76)(72,77)(83,88)(84,89)(85,90)(86,91)(87,92);;
s2 := ( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,38)(19,39)(20,40)(21,41)(22,42)
(23,33)(24,34)(25,35)(26,36)(27,37)(28,43)(29,44)(30,45)(31,46)(32,47)(48,53)
(49,54)(50,55)(51,56)(52,57)(63,83)(64,84)(65,85)(66,86)(67,87)(68,78)(69,79)
(70,80)(71,81)(72,82)(73,88)(74,89)(75,90)(76,91)(77,92);;
s3 := ( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)
(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)
(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)(57,74)
(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)
(87,89);;
s4 := ( 3,49)( 4,48)( 5,52)( 6,51)( 7,50)( 8,54)( 9,53)(10,57)(11,56)(12,55)
(13,59)(14,58)(15,62)(16,61)(17,60)(18,64)(19,63)(20,67)(21,66)(22,65)(23,69)
(24,68)(25,72)(26,71)(27,70)(28,74)(29,73)(30,77)(31,76)(32,75)(33,79)(34,78)
(35,82)(36,81)(37,80)(38,84)(39,83)(40,87)(41,86)(42,85)(43,89)(44,88)(45,92)
(46,91)(47,90);;
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, 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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope