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}*1440a
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, {2,6,2,10}*480
5-fold quotients : {2,6,6,2}*288a
6-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
9-fold quotients : {2,2,2,10}*160
12-fold quotients : {2,3,2,5}*120
15-fold quotients : {2,2,6,2}*96, {2,6,2,2}*96
18-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,3,2}*48, {2,3,2,2}*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)( 8,23)( 9,27)(10,26)(11,25)(12,24)
(13,28)(14,32)(15,31)(16,30)(17,29)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)
(48,63)(49,67)(50,66)(51,65)(52,64)(53,68)(54,72)(55,71)(56,70)(57,69)(58,73)
(59,77)(60,76)(61,75)(62,74)(79,82)(80,81)(84,87)(85,86)(89,92)(90,91);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
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)( 8,23)( 9,27)(10,26)(11,25)
(12,24)(13,28)(14,32)(15,31)(16,30)(17,29)(34,37)(35,36)(39,42)(40,41)(44,47)
(45,46)(48,63)(49,67)(50,66)(51,65)(52,64)(53,68)(54,72)(55,71)(56,70)(57,69)
(58,73)(59,77)(60,76)(61,75)(62,74)(79,82)(80,81)(84,87)(85,86)(89,92)(90,91);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, 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