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

Overview

Group: SmallGroup(288,951)
Rank: 4
Schläfli Type: {2,6,12}
Vertices, edges, …: 2, 6, 36, 12
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

{2,6,6}*144a

3-fold

6-fold

9-fold

{2,2,4}*32

12-fold

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