Polytope of Type {4,6,4} with group SmallGroup(576,8399)

Overview

Group: SmallGroup(576,8399)
Rank: 4
Schläfli Type: {4,6,4}
Vertices, edges, …: 4, 36, 36, 12
Order of s₀s₁s₂s₃: 4
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{4,6|2},{6,4}₄}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{2,6,4}*288

4-fold

{2,6,4}*144

9-fold

{4,2,4}*64

18-fold

36-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2*s3*s2)^2> of order 3

4 facets

4 of {4,6}*48a

4 vertex figures

4 of 3-fold non-regular quotient of {6,4}*144

P/N, where N=<s1*s3*s2*s1*s2*s3> of order 3

8 facets

2 of {4,6}*48a
6 of {4,2}*16

4 vertex figures

4 of 3-fold non-regular quotient of {6,4}*144

Representations

Permutation Representation (GAP)

s0 := ( 1,19)( 2,20)( 3,21)( 4,22)( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36);;
s1 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(19,28)(20,30)(21,29)(22,34)(23,36)(24,35)(25,31)(26,33)(27,32);;
s2 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33);;
s3 := ( 2, 4)( 3, 7)( 6, 8)(11,13)(12,16)(15,17)(20,22)(21,25)(24,26)(29,31)(30,34)(33,35);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(36)!( 1,19)( 2,20)( 3,21)( 4,22)( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36);
s1 := Sym(36)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(19,28)(20,30)(21,29)(22,34)(23,36)(24,35)(25,31)(26,33)(27,32);
s2 := Sym(36)!( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33);
s3 := Sym(36)!( 2, 4)( 3, 7)( 6, 8)(11,13)(12,16)(15,17)(20,22)(21,25)(24,26)(29,31)(30,34)(33,35);
poly := sub<Sym(36)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.