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}*1440c
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) :
   3-fold quotients : {2,10,6,2}*480
   5-fold quotients : {2,2,6,6}*288c
   9-fold quotients : {2,10,2,2}*160
   10-fold quotients : {2,2,3,6}*144
   15-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,5,2,2}*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 := ( 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)(18,34)(19,33)(20,37)
(21,36)(22,35)(23,44)(24,43)(25,47)(26,46)(27,45)(28,39)(29,38)(30,42)(31,41)
(32,40)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,79)(64,78)(65,82)
(66,81)(67,80)(68,89)(69,88)(70,92)(71,91)(72,90)(73,84)(74,83)(75,87)(76,86)
(77,85);;
s3 := ( 3,68)( 4,69)( 5,70)( 6,71)( 7,72)( 8,63)( 9,64)(10,65)(11,66)(12,67)
(13,73)(14,74)(15,75)(16,76)(17,77)(18,53)(19,54)(20,55)(21,56)(22,57)(23,48)
(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62)(33,83)(34,84)
(35,85)(36,86)(37,87)(38,78)(39,79)(40,80)(41,81)(42,82)(43,88)(44,89)(45,90)
(46,91)(47,92);;
s4 := ( 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);;
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*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
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)(18,34)(19,33)
(20,37)(21,36)(22,35)(23,44)(24,43)(25,47)(26,46)(27,45)(28,39)(29,38)(30,42)
(31,41)(32,40)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,79)(64,78)
(65,82)(66,81)(67,80)(68,89)(69,88)(70,92)(71,91)(72,90)(73,84)(74,83)(75,87)
(76,86)(77,85);
s3 := Sym(92)!( 3,68)( 4,69)( 5,70)( 6,71)( 7,72)( 8,63)( 9,64)(10,65)(11,66)
(12,67)(13,73)(14,74)(15,75)(16,76)(17,77)(18,53)(19,54)(20,55)(21,56)(22,57)
(23,48)(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62)(33,83)
(34,84)(35,85)(36,86)(37,87)(38,78)(39,79)(40,80)(41,81)(42,82)(43,88)(44,89)
(45,90)(46,91)(47,92);
s4 := 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);
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*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope