Polytope of Type {6,6,12} with group SmallGroup(1920,240594)

Overview

Group: SmallGroup(1920,240594)
Rank: 4
Schläfli Type: {6,6,12}
Vertices, edges, …: 10, 40, 80, 20
Order of s₀s₁s₂s₃: 20
Order of s₀s₁s₂s₃s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

{3,3,3}*120

60-fold

{2,2,4}*32

120-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 6, 8)( 7, 9)(10,12)(11,13)(14,16)(15,17)(18,20)(19,21)(22,24)(23,25)(26,28)(27,29)(30,32)(31,33)(34,36)(35,37);;
s1 := ( 4, 5)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);;
s2 := ( 2, 5)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37);;
s3 := ( 1, 2)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,31)(15,30)(16,33)(17,32)(18,35)(19,34)(20,37)(21,36);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(37)!( 3, 4)( 6, 8)( 7, 9)(10,12)(11,13)(14,16)(15,17)(18,20)(19,21)(22,24)(23,25)(26,28)(27,29)(30,32)(31,33)(34,36)(35,37);
s1 := Sym(37)!( 4, 5)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
s2 := Sym(37)!( 2, 5)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37);
s3 := Sym(37)!( 1, 2)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,31)(15,30)(16,33)(17,32)(18,35)(19,34)(20,37)(21,36);
poly := sub<Sym(37)|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, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 >;

References