Polytope of Type {12,6,2} with group SmallGroup(288,951)

Overview

Group: SmallGroup(288,951)
Rank: 4
Schläfli Type: {12,6,2}
Vertices, edges, …: 12, 36, 6, 2
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{6,6,2}*144c

3-fold

{12,2,2}*96

4-fold

{3,6,2}*72

6-fold

{6,2,2}*48

9-fold

{4,2,2}*32

12-fold

{3,2,2}*24

18-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

Permutation Representation (GAP)

s0 := ( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,64)(20,66)(21,65)(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59);;
s1 := ( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)(21,42)(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)(33,48)(34,53)(35,52)(36,54);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72);;
s3 := (73,74);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(74)!( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,64)(20,66)(21,65)(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59);
s1 := Sym(74)!( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)(21,42)(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)(33,48)(34,53)(35,52)(36,54);
s2 := Sym(74)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72);
s3 := Sym(74)!(73,74);
poly := sub<Sym(74)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;