Polytope of Type {2,4,6} with group SmallGroup(288,1031)

Overview

Group: SmallGroup(288,1031)
Rank: 4
Schläfli Type: {2,4,6}
Vertices, edges, …: 2, 12, 36, 18
Order of s₀s₁s₂s₃: 4
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

{2,4,6}*144

9-fold

{2,4,2}*32

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