Polytope of Type {2,6,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,4}*576c
if this polytope has a name.
Group : SmallGroup(576,8589)
Rank : 5
Schlafli Type : {2,6,6,4}
Number of vertices, edges, etc : 2, 6, 18, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,6,4,2} of size 1152
Vertex Figure Of :
{2,2,6,6,4} of size 1152
{3,2,6,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,6,4}*288, {2,6,6,2}*288c
3-fold quotients : {2,6,2,4}*192
4-fold quotients : {2,3,6,2}*144
6-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
9-fold quotients : {2,2,2,4}*64
12-fold quotients : {2,3,2,2}*48
18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,12,4}*1152c, {4,6,6,4}*1152b, {2,12,6,4}*1152c, {2,6,6,8}*1152c
3-fold covers : {2,18,6,4}*1728b, {2,6,6,4}*1728c, {2,6,6,12}*1728e, {6,6,6,4}*1728g, {6,6,6,4}*1728h, {2,6,6,4}*1728h
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)(24,27)
(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)(49,50)
(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);;
s2 := ( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)(12,52)
(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,61)(22,60)(23,62)
(24,58)(25,57)(26,59)(27,64)(28,63)(29,65)(30,70)(31,69)(32,71)(33,67)(34,66)
(35,68)(36,73)(37,72)(38,74);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)
(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)
(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);;
s4 := ( 3,21)( 4,22)( 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)(39,57)(40,58)(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);;
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,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)
(24,27)(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)
(49,50)(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);
s2 := Sym(74)!( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)
(12,52)(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,61)(22,60)
(23,62)(24,58)(25,57)(26,59)(27,64)(28,63)(29,65)(30,70)(31,69)(32,71)(33,67)
(34,66)(35,68)(36,73)(37,72)(38,74);
s3 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)
(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)
(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);
s4 := Sym(74)!( 3,21)( 4,22)( 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)(39,57)(40,58)
(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);
poly := sub<Sym(74)|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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 >;
to this polytope