Polytope of Type {6,3} with group SmallGroup(588,35) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(588,35)
Rank: 3
Schläfli Type: {6,3}
Vertices, edges, …: 98, 147, 49
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 6
Also known as: {6,3}_(7,0), {6,3}₁₄. if this polytope has another name.

Special Properties

Toroidal
Locally Spherical
Orientable

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

{6,6}*1176a

3-fold

{6,3}*1764

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)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 7

7 facets

7 of {6}*12

14 vertex figures

14 of {3}*6

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 7

7 facets

7 of {6}*12

14 vertex figures

14 of {3}*6

Representations

Permutation Representation (GAP)

s0 := ( 2,22)( 3,43)( 4,15)( 5,36)( 6, 8)( 7,29)( 9,27)(10,48)(11,20)(12,41)(14,34)(16,25)(17,46)(19,39)(21,32)(24,44)(26,37)(28,30)(31,49)(33,42)(38,47);;
s1 := ( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)(13,37)(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)(42,48);;
s2 := ( 1,23)( 3,30)( 4, 9)( 5,37)( 6,16)( 7,44)( 8,25)(10,32)(12,39)(13,18)(14,46)(15,27)(17,34)(19,41)(21,48)(24,29)(26,36)(28,43)(33,38)(35,45)(42,47);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

s0 := Sym(49)!( 2,22)( 3,43)( 4,15)( 5,36)( 6, 8)( 7,29)( 9,27)(10,48)(11,20)(12,41)(14,34)(16,25)(17,46)(19,39)(21,32)(24,44)(26,37)(28,30)(31,49)(33,42)(38,47);
s1 := Sym(49)!( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)(13,37)(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)(42,48);
s2 := Sym(49)!( 1,23)( 3,30)( 4, 9)( 5,37)( 6,16)( 7,44)( 8,25)(10,32)(12,39)(13,18)(14,46)(15,27)(17,34)(19,41)(21,48)(24,29)(26,36)(28,43)(33,38)(35,45)(42,47);
poly := sub<Sym(49)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

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

References

None.

to this polytope.