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