Polytope of Type {2,2,3,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,6,4}*576
if this polytope has a name.
Group : SmallGroup(576,8589)
Rank : 6
Schlafli Type : {2,2,3,6,4}
Number of vertices, edges, etc : 2, 2, 3, 9, 12, 4
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,3,6,4,2} of size 1152
Vertex Figure Of :
{2,2,2,3,6,4} of size 1152
{3,2,2,3,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,3,6,2}*288
3-fold quotients : {2,2,3,2,4}*192
6-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,3,6,4}*1152, {2,2,3,6,8}*1152, {2,2,6,6,4}*1152c
3-fold covers : {2,2,9,6,4}*1728, {2,2,3,6,4}*1728a, {2,2,3,6,12}*1728b, {2,6,3,6,4}*1728, {6,2,3,6,4}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,41)( 6,43)( 7,42)( 8,47)( 9,49)(10,48)(11,44)(12,46)(13,45)(14,50)
(15,52)(16,51)(17,56)(18,58)(19,57)(20,53)(21,55)(22,54)(23,59)(24,61)(25,60)
(26,65)(27,67)(28,66)(29,62)(30,64)(31,63)(32,68)(33,70)(34,69)(35,74)(36,76)
(37,75)(38,71)(39,73)(40,72);;
s3 := ( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)(14,54)
(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,63)(24,62)(25,64)
(26,60)(27,59)(28,61)(29,66)(30,65)(31,67)(32,72)(33,71)(34,73)(35,69)(36,68)
(37,70)(38,75)(39,74)(40,76);;
s4 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)(26,35)
(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)
(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);;
s5 := ( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)
(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(41,59)(42,60)(43,61)
(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)
(55,73)(56,74)(57,75)(58,76);;
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, s1*s2*s1*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,
s2*s3*s2*s3*s2*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 5,41)( 6,43)( 7,42)( 8,47)( 9,49)(10,48)(11,44)(12,46)(13,45)
(14,50)(15,52)(16,51)(17,56)(18,58)(19,57)(20,53)(21,55)(22,54)(23,59)(24,61)
(25,60)(26,65)(27,67)(28,66)(29,62)(30,64)(31,63)(32,68)(33,70)(34,69)(35,74)
(36,76)(37,75)(38,71)(39,73)(40,72);
s3 := Sym(76)!( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)
(14,54)(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,63)(24,62)
(25,64)(26,60)(27,59)(28,61)(29,66)(30,65)(31,67)(32,72)(33,71)(34,73)(35,69)
(36,68)(37,70)(38,75)(39,74)(40,76);
s4 := Sym(76)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)
(26,35)(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)
(57,58)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);
s5 := Sym(76)!( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)
(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(41,59)(42,60)
(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)
(54,72)(55,73)(56,74)(57,75)(58,76);
poly := sub<Sym(76)|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,
s1*s2*s1*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, s2*s3*s2*s3*s2*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 >;
to this polytope