Polytope of Type {4,6,3,4} with group SmallGroup(1728,47847)

Overview

Group: SmallGroup(1728,47847)
Rank: 5
Schläfli Type: {4,6,3,4}
Vertices, edges, …: 12, 36, 27, 6, 4
Order of s₀s₁s₂s₃s₄: 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

9-fold

{4,2,3,4}*192

18-fold

{2,2,3,4}*96

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1*s2*s1)^2> of order 3

4 facets

4 of 3-fold non-regular quotient of {4,6,3}*432b

4 vertex figures

4 of {6,3,4}*144

P/N, where N=<s0*s1*s2*s1*s0*s2> of order 3

4 facets

4 of 3-fold non-regular quotient of {4,6,3}*432b

8 vertex figures

2 of {6,3,4}*144
6 of {2,3,4}*48

Representations

Permutation Representation (GAP)

s0 := ( 5,29)( 6,30)( 7,31)( 8,32)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28);;
s1 := (13,33)(14,34)(15,35)(16,36)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32);;
s2 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,13)( 6,14)( 7,16)( 8,15)( 9,21)(10,22)(11,24)(12,23)(25,29)(26,30)(27,32)(28,31)(35,36);;
s3 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,25)(14,28)(15,27)(16,26)(17,33)(18,36)(19,35)(20,34)(21,29)(22,32)(23,31)(24,30);;
s4 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(36)!( 5,29)( 6,30)( 7,31)( 8,32)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28);
s1 := Sym(36)!(13,33)(14,34)(15,35)(16,36)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32);
s2 := Sym(36)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,13)( 6,14)( 7,16)( 8,15)( 9,21)(10,22)(11,24)(12,23)(25,29)(26,30)(27,32)(28,31)(35,36);
s3 := Sym(36)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,25)(14,28)(15,27)(16,26)(17,33)(18,36)(19,35)(20,34)(21,29)(22,32)(23,31)(24,30);
s4 := Sym(36)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);
poly := sub<Sym(36)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.