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

Overview

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

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

Permutation Representation (Magma)

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