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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6,6}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {2,10,6,6}
Number of vertices, edges, etc : 2, 10, 30, 18, 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 : {2,10,6,3}*720
   3-fold quotients : {2,10,2,6}*480
   5-fold quotients : {2,2,6,6}*288b
   6-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
   9-fold quotients : {2,10,2,2}*160
   10-fold quotients : {2,2,6,3}*144
   12-fold quotients : {2,5,2,3}*120
   15-fold quotients : {2,2,2,6}*96
   18-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,2,3}*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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)(54,57)
(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76)(79,82)(80,81)
(84,87)(85,86)(89,92)(90,91);;
s2 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)
(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45)
(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,64)(65,67)(68,74)(69,73)
(70,77)(71,76)(72,75)(78,79)(80,82)(83,89)(84,88)(85,92)(86,91)(87,90);;
s3 := ( 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);;
s4 := ( 3,63)( 4,64)( 5,65)( 6,66)( 7,67)( 8,73)( 9,74)(10,75)(11,76)(12,77)
(13,68)(14,69)(15,70)(16,71)(17,72)(18,48)(19,49)(20,50)(21,51)(22,52)(23,58)
(24,59)(25,60)(26,61)(27,62)(28,53)(29,54)(30,55)(31,56)(32,57)(33,78)(34,79)
(35,80)(36,81)(37,82)(38,88)(39,89)(40,90)(41,91)(42,92)(43,83)(44,84)(45,85)
(46,86)(47,87);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*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, 
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)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)
(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76)(79,82)
(80,81)(84,87)(85,86)(89,92)(90,91);
s2 := Sym(92)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)
(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)
(42,45)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,64)(65,67)(68,74)
(69,73)(70,77)(71,76)(72,75)(78,79)(80,82)(83,89)(84,88)(85,92)(86,91)(87,90);
s3 := 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);
s4 := Sym(92)!( 3,63)( 4,64)( 5,65)( 6,66)( 7,67)( 8,73)( 9,74)(10,75)(11,76)
(12,77)(13,68)(14,69)(15,70)(16,71)(17,72)(18,48)(19,49)(20,50)(21,51)(22,52)
(23,58)(24,59)(25,60)(26,61)(27,62)(28,53)(29,54)(30,55)(31,56)(32,57)(33,78)
(34,79)(35,80)(36,81)(37,82)(38,88)(39,89)(40,90)(41,91)(42,92)(43,83)(44,84)
(45,85)(46,86)(47,87);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope