Polytope of Type {2,18,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,6,3}*1296b
if this polytope has a name.
Group : SmallGroup(1296,2984)
Rank : 5
Schlafli Type : {2,18,6,3}
Number of vertices, edges, etc : 2, 18, 54, 9, 3
Order of s0s1s2s3s4 : 18
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 : {2,18,2,3}*432, {2,6,6,3}*432b
6-fold quotients : {2,9,2,3}*216
9-fold quotients : {2,2,6,3}*144, {2,6,2,3}*144
18-fold quotients : {2,3,2,3}*72
27-fold quotients : {2,2,2,3}*48
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)(30,59)
(31,58)(32,57)(33,62)(34,61)(35,60)(36,65)(37,64)(38,63)(39,68)(40,67)(41,66)
(42,71)(43,70)(44,69)(45,74)(46,73)(47,72)(48,77)(49,76)(50,75)(51,80)(52,79)
(53,78)(54,83)(55,82)(56,81);;
s2 := ( 3,30)( 4,32)( 5,31)( 6,36)( 7,38)( 8,37)( 9,33)(10,35)(11,34)(12,39)
(13,41)(14,40)(15,45)(16,47)(17,46)(18,42)(19,44)(20,43)(21,48)(22,50)(23,49)
(24,54)(25,56)(26,55)(27,51)(28,53)(29,52)(57,59)(60,65)(61,64)(62,63)(66,68)
(69,74)(70,73)(71,72)(75,77)(78,83)(79,82)(80,81);;
s3 := ( 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);;
s4 := ( 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]);;
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,
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(83)!(1,2);
s1 := Sym(83)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(30,59)(31,58)(32,57)(33,62)(34,61)(35,60)(36,65)(37,64)(38,63)(39,68)(40,67)
(41,66)(42,71)(43,70)(44,69)(45,74)(46,73)(47,72)(48,77)(49,76)(50,75)(51,80)
(52,79)(53,78)(54,83)(55,82)(56,81);
s2 := Sym(83)!( 3,30)( 4,32)( 5,31)( 6,36)( 7,38)( 8,37)( 9,33)(10,35)(11,34)
(12,39)(13,41)(14,40)(15,45)(16,47)(17,46)(18,42)(19,44)(20,43)(21,48)(22,50)
(23,49)(24,54)(25,56)(26,55)(27,51)(28,53)(29,52)(57,59)(60,65)(61,64)(62,63)
(66,68)(69,74)(70,73)(71,72)(75,77)(78,83)(79,82)(80,81);
s3 := 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);
s4 := 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>;
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope