Polytope of Type {2,36,2} with group SmallGroup(288,354)

Overview

Group: SmallGroup(288,354)
Rank: 4
Schläfli Type: {2,36,2}
Vertices, edges, …: 2, 36, 36, 2
Order of s₀s₁s₂s₃: 36
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat
Self-Dual

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,18,2}*144

3-fold

{2,12,2}*96

4-fold

{2,9,2}*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 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)(20,31)(22,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);;
s3 := (39,40);;
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, 
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*s1*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*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(40)!(1,2);
s1 := Sym(40)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);
s2 := Sym(40)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)(20,31)(22,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);
s3 := Sym(40)!(39,40);
poly := sub<Sym(40)|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, 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*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;