Polytope of Type {2,3,6,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,6,3}*1296
if this polytope has a name.
Group : SmallGroup(1296,3585)
Rank : 6
Schlafli Type : {2,3,6,6,3}
Number of vertices, edges, etc : 2, 3, 9, 18, 9, 3
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,3,2,6,3}*432, {2,3,6,2,3}*432
9-fold quotients : {2,3,2,2,3}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(30,57)
(31,59)(32,58)(33,60)(34,62)(35,61)(36,63)(37,65)(38,64)(39,66)(40,68)(41,67)
(42,69)(43,71)(44,70)(45,72)(46,74)(47,73)(48,75)(49,77)(50,76)(51,78)(52,80)
(53,79)(54,81)(55,83)(56,82);;
s2 := ( 3,31)( 4,30)( 5,32)( 6,34)( 7,33)( 8,35)( 9,37)(10,36)(11,38)(12,40)
(13,39)(14,41)(15,43)(16,42)(17,44)(18,46)(19,45)(20,47)(21,49)(22,48)(23,50)
(24,52)(25,51)(26,53)(27,55)(28,54)(29,56)(57,58)(60,61)(63,64)(66,67)(69,70)
(72,73)(75,76)(78,79)(81,82);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(30,57)
(31,58)(32,59)(33,63)(34,64)(35,65)(36,60)(37,61)(38,62)(39,66)(40,67)(41,68)
(42,72)(43,73)(44,74)(45,69)(46,70)(47,71)(48,75)(49,76)(50,77)(51,81)(52,82)
(53,83)(54,78)(55,79)(56,80);;
s4 := ( 3, 6)( 4, 7)( 5, 8)(12,24)(13,25)(14,26)(15,21)(16,22)(17,23)(18,27)
(19,28)(20,29)(30,33)(31,34)(32,35)(39,51)(40,52)(41,53)(42,48)(43,49)(44,50)
(45,54)(46,55)(47,56)(57,60)(58,61)(59,62)(66,78)(67,79)(68,80)(69,75)(70,76)
(71,77)(72,81)(73,82)(74,83);;
s5 := ( 3,12)( 4,13)( 5,14)( 6,18)( 7,19)( 8,20)( 9,15)(10,16)(11,17)(24,27)
(25,28)(26,29)(30,39)(31,40)(32,41)(33,45)(34,46)(35,47)(36,42)(37,43)(38,44)
(51,54)(52,55)(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)
(65,71)(78,81)(79,82)(80,83);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s1*s2*s1*s2*s1*s2,
s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(83)!(1,2);
s1 := Sym(83)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(30,57)(31,59)(32,58)(33,60)(34,62)(35,61)(36,63)(37,65)(38,64)(39,66)(40,68)
(41,67)(42,69)(43,71)(44,70)(45,72)(46,74)(47,73)(48,75)(49,77)(50,76)(51,78)
(52,80)(53,79)(54,81)(55,83)(56,82);
s2 := Sym(83)!( 3,31)( 4,30)( 5,32)( 6,34)( 7,33)( 8,35)( 9,37)(10,36)(11,38)
(12,40)(13,39)(14,41)(15,43)(16,42)(17,44)(18,46)(19,45)(20,47)(21,49)(22,48)
(23,50)(24,52)(25,51)(26,53)(27,55)(28,54)(29,56)(57,58)(60,61)(63,64)(66,67)
(69,70)(72,73)(75,76)(78,79)(81,82);
s3 := Sym(83)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(30,57)(31,58)(32,59)(33,63)(34,64)(35,65)(36,60)(37,61)(38,62)(39,66)(40,67)
(41,68)(42,72)(43,73)(44,74)(45,69)(46,70)(47,71)(48,75)(49,76)(50,77)(51,81)
(52,82)(53,83)(54,78)(55,79)(56,80);
s4 := Sym(83)!( 3, 6)( 4, 7)( 5, 8)(12,24)(13,25)(14,26)(15,21)(16,22)(17,23)
(18,27)(19,28)(20,29)(30,33)(31,34)(32,35)(39,51)(40,52)(41,53)(42,48)(43,49)
(44,50)(45,54)(46,55)(47,56)(57,60)(58,61)(59,62)(66,78)(67,79)(68,80)(69,75)
(70,76)(71,77)(72,81)(73,82)(74,83);
s5 := Sym(83)!( 3,12)( 4,13)( 5,14)( 6,18)( 7,19)( 8,20)( 9,15)(10,16)(11,17)
(24,27)(25,28)(26,29)(30,39)(31,40)(32,41)(33,45)(34,46)(35,47)(36,42)(37,43)
(38,44)(51,54)(52,55)(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)
(64,70)(65,71)(78,81)(79,82)(80,83);
poly := sub<Sym(83)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 >;
to this polytope