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}*1440a
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 : {2,10,2,6}*480, {2,10,6,2}*480
5-fold quotients : {2,2,6,6}*288a
6-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
9-fold quotients : {2,10,2,2}*160
12-fold quotients : {2,5,2,3}*120
15-fold quotients : {2,2,2,6}*96, {2,2,6,2}*96
18-fold quotients : {2,5,2,2}*80
30-fold quotients : {2,2,2,3}*48, {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)(18,19)(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)( 8,68)( 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,
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)( 8,68)( 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, 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