Polytope of Type {3,2,3,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,3,6,4}*864
if this polytope has a name.
Group : SmallGroup(864,4406)
Rank : 6
Schlafli Type : {3,2,3,6,4}
Number of vertices, edges, etc : 3, 3, 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 :
{3,2,3,6,4,2} of size 1728
Vertex Figure Of :
{2,3,2,3,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,3,6,2}*432
3-fold quotients : {3,2,3,2,4}*288
6-fold quotients : {3,2,3,2,2}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,3,6,8}*1728, {3,2,6,6,4}*1728c, {6,2,3,6,4}*1728
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,40)( 5,42)( 6,41)( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)
(14,51)(15,50)(16,55)(17,57)(18,56)(19,52)(20,54)(21,53)(22,58)(23,60)(24,59)
(25,64)(26,66)(27,65)(28,61)(29,63)(30,62)(31,67)(32,69)(33,68)(34,73)(35,75)
(36,74)(37,70)(38,72)(39,71);;
s3 := ( 4,44)( 5,43)( 6,45)( 7,41)( 8,40)( 9,42)(10,47)(11,46)(12,48)(13,53)
(14,52)(15,54)(16,50)(17,49)(18,51)(19,56)(20,55)(21,57)(22,62)(23,61)(24,63)
(25,59)(26,58)(27,60)(28,65)(29,64)(30,66)(31,71)(32,70)(33,72)(34,68)(35,67)
(36,69)(37,74)(38,73)(39,75);;
s4 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,31)(23,33)(24,32)(25,34)
(26,36)(27,35)(28,37)(29,39)(30,38)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)
(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74);;
s5 := ( 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)(21,39)(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)(57,75);;
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*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, s0*s1*s0*s1*s0*s1,
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(75)!(2,3);
s1 := Sym(75)!(1,2);
s2 := Sym(75)!( 4,40)( 5,42)( 6,41)( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)
(13,49)(14,51)(15,50)(16,55)(17,57)(18,56)(19,52)(20,54)(21,53)(22,58)(23,60)
(24,59)(25,64)(26,66)(27,65)(28,61)(29,63)(30,62)(31,67)(32,69)(33,68)(34,73)
(35,75)(36,74)(37,70)(38,72)(39,71);
s3 := Sym(75)!( 4,44)( 5,43)( 6,45)( 7,41)( 8,40)( 9,42)(10,47)(11,46)(12,48)
(13,53)(14,52)(15,54)(16,50)(17,49)(18,51)(19,56)(20,55)(21,57)(22,62)(23,61)
(24,63)(25,59)(26,58)(27,60)(28,65)(29,64)(30,66)(31,71)(32,70)(33,72)(34,68)
(35,67)(36,69)(37,74)(38,73)(39,75);
s4 := Sym(75)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,31)(23,33)(24,32)
(25,34)(26,36)(27,35)(28,37)(29,39)(30,38)(41,42)(44,45)(47,48)(50,51)(53,54)
(56,57)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74);
s5 := Sym(75)!( 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)(21,39)(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)(57,75);
poly := sub<Sym(75)|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*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,
s0*s1*s0*s1*s0*s1, 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