Polytope of Type {2,6,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,3}*576
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 5
Schlafli Type : {2,6,6,3}
Number of vertices, edges, etc : 2, 6, 24, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,6,3,2} of size 1152
Vertex Figure Of :
{2,2,6,6,3} of size 1152
{3,2,6,6,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,2,6,3}*192
6-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,6,3}*1152, {4,6,6,3}*1152a, {2,6,12,3}*1152, {2,6,6,6}*1152a
3-fold covers : {2,18,6,3}*1728, {6,6,6,3}*1728a, {6,6,6,3}*1728b, {2,6,6,3}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)(67,71)
(68,72)(69,73)(70,74);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)(19,27)
(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)(42,46)
(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)
(61,72)(62,74);;
s3 := ( 3,51)( 4,52)( 5,54)( 6,53)( 7,55)( 8,56)( 9,58)(10,57)(11,59)(12,60)
(13,62)(14,61)(15,39)(16,40)(17,42)(18,41)(19,43)(20,44)(21,46)(22,45)(23,47)
(24,48)(25,50)(26,49)(27,63)(28,64)(29,66)(30,65)(31,67)(32,68)(33,70)(34,69)
(35,71)(36,72)(37,74)(38,73);;
s4 := ( 3,42)( 4,40)( 5,41)( 6,39)( 7,46)( 8,44)( 9,45)(10,43)(11,50)(12,48)
(13,49)(14,47)(15,66)(16,64)(17,65)(18,63)(19,70)(20,68)(21,69)(22,67)(23,74)
(24,72)(25,73)(26,71)(27,54)(28,52)(29,53)(30,51)(31,58)(32,56)(33,57)(34,55)
(35,62)(36,60)(37,61)(38,59);;
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,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)
(67,71)(68,72)(69,73)(70,74);
s2 := Sym(74)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)
(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)
(42,46)(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)
(60,73)(61,72)(62,74);
s3 := Sym(74)!( 3,51)( 4,52)( 5,54)( 6,53)( 7,55)( 8,56)( 9,58)(10,57)(11,59)
(12,60)(13,62)(14,61)(15,39)(16,40)(17,42)(18,41)(19,43)(20,44)(21,46)(22,45)
(23,47)(24,48)(25,50)(26,49)(27,63)(28,64)(29,66)(30,65)(31,67)(32,68)(33,70)
(34,69)(35,71)(36,72)(37,74)(38,73);
s4 := Sym(74)!( 3,42)( 4,40)( 5,41)( 6,39)( 7,46)( 8,44)( 9,45)(10,43)(11,50)
(12,48)(13,49)(14,47)(15,66)(16,64)(17,65)(18,63)(19,70)(20,68)(21,69)(22,67)
(23,74)(24,72)(25,73)(26,71)(27,54)(28,52)(29,53)(30,51)(31,58)(32,56)(33,57)
(34,55)(35,62)(36,60)(37,61)(38,59);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope