Polytope of Type {6,6,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,10,2}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {6,6,10,2}
Number of vertices, edges, etc : 6, 18, 30, 10, 2
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 : {2,6,10,2}*480, {6,2,10,2}*480
5-fold quotients : {6,6,2,2}*288a
6-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
9-fold quotients : {2,2,10,2}*160
12-fold quotients : {3,2,5,2}*120
15-fold quotients : {2,6,2,2}*96, {6,2,2,2}*96
18-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,3,2,2}*48, {3,2,2,2}*48
45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)
(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60)(66,71)
(67,72)(68,73)(69,74)(70,75)(81,86)(82,87)(83,88)(84,89)(85,90);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,36)(17,37)(18,38)(19,39)(20,40)
(21,31)(22,32)(23,33)(24,34)(25,35)(26,41)(27,42)(28,43)(29,44)(30,45)(46,51)
(47,52)(48,53)(49,54)(50,55)(61,81)(62,82)(63,83)(64,84)(65,85)(66,76)(67,77)
(68,78)(69,79)(70,80)(71,86)(72,87)(73,88)(74,89)(75,90);;
s2 := ( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)
(11,26)(12,30)(13,29)(14,28)(15,27)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)
(46,61)(47,65)(48,64)(49,63)(50,62)(51,66)(52,70)(53,69)(54,68)(55,67)(56,71)
(57,75)(58,74)(59,73)(60,72)(77,80)(78,79)(82,85)(83,84)(87,90)(88,89);;
s3 := ( 1,47)( 2,46)( 3,50)( 4,49)( 5,48)( 6,52)( 7,51)( 8,55)( 9,54)(10,53)
(11,57)(12,56)(13,60)(14,59)(15,58)(16,62)(17,61)(18,65)(19,64)(20,63)(21,67)
(22,66)(23,70)(24,69)(25,68)(26,72)(27,71)(28,75)(29,74)(30,73)(31,77)(32,76)
(33,80)(34,79)(35,78)(36,82)(37,81)(38,85)(39,84)(40,83)(41,87)(42,86)(43,90)
(44,89)(45,88);;
s4 := (91,92);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(92)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)
(25,30)(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60)
(66,71)(67,72)(68,73)(69,74)(70,75)(81,86)(82,87)(83,88)(84,89)(85,90);
s1 := Sym(92)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,36)(17,37)(18,38)(19,39)
(20,40)(21,31)(22,32)(23,33)(24,34)(25,35)(26,41)(27,42)(28,43)(29,44)(30,45)
(46,51)(47,52)(48,53)(49,54)(50,55)(61,81)(62,82)(63,83)(64,84)(65,85)(66,76)
(67,77)(68,78)(69,79)(70,80)(71,86)(72,87)(73,88)(74,89)(75,90);
s2 := Sym(92)!( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,21)( 7,25)( 8,24)( 9,23)
(10,22)(11,26)(12,30)(13,29)(14,28)(15,27)(32,35)(33,34)(37,40)(38,39)(42,45)
(43,44)(46,61)(47,65)(48,64)(49,63)(50,62)(51,66)(52,70)(53,69)(54,68)(55,67)
(56,71)(57,75)(58,74)(59,73)(60,72)(77,80)(78,79)(82,85)(83,84)(87,90)(88,89);
s3 := Sym(92)!( 1,47)( 2,46)( 3,50)( 4,49)( 5,48)( 6,52)( 7,51)( 8,55)( 9,54)
(10,53)(11,57)(12,56)(13,60)(14,59)(15,58)(16,62)(17,61)(18,65)(19,64)(20,63)
(21,67)(22,66)(23,70)(24,69)(25,68)(26,72)(27,71)(28,75)(29,74)(30,73)(31,77)
(32,76)(33,80)(34,79)(35,78)(36,82)(37,81)(38,85)(39,84)(40,83)(41,87)(42,86)
(43,90)(44,89)(45,88);
s4 := Sym(92)!(91,92);
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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope