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}*144c

3-fold

{2,12,2}*96

4-fold

{2,3,6}*72

6-fold

{2,6,2}*48

9-fold

{2,4,2}*32

12-fold

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