Polytope of Type {12,6,3} with group SmallGroup(1152,155790)

Overview

Group: SmallGroup(1152,155790)
Rank: 4
Schläfli Type: {12,6,3}
Vertices, edges, …: 24, 96, 24, 4
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Orientable
Flat

Quotients maximal quotients in bold

3-fold

{4,6,3}*384b

4-fold

{6,6,3}*288

6-fold

{4,3,3}*192

12-fold

{2,6,3}*96

24-fold

{2,3,3}*48

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*(s2*s1)^2*s0*(s1*s2)^2> of order 2

4 facets

4 of 2-fold non-regular quotient of {12,6}*288a

12 vertex figures

12 of {6,3}*48

Representations

Permutation Representation (GAP)

s0 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,33)(18,34)(19,35)(20,36)(21,38)(22,37)(23,40)(24,39)(25,43)(26,44)(27,41)(28,42)(29,48)(30,47)(31,46)(32,45);;
s1 := ( 1,21)( 2,22)( 3,24)( 4,23)( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48);;
s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44);;
s3 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47);;
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*s3*s2*s3*s2*s3, 
s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s3*s0*s2*s1*s0*s1*s2*s1*s3*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(48)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,33)(18,34)(19,35)(20,36)(21,38)(22,37)(23,40)(24,39)(25,43)(26,44)(27,41)(28,42)(29,48)(30,47)(31,46)(32,45);
s1 := Sym(48)!( 1,21)( 2,22)( 3,24)( 4,23)( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48);
s2 := Sym(48)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44);
s3 := Sym(48)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47);
poly := sub<Sym(48)|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*s3*s2*s3*s2*s3, s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s3*s0*s2*s1*s0*s1*s2*s1*s3*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.