Polytope of Type {14,7} with group SmallGroup(1372,16)

Overview

Group: SmallGroup(1372,16)
Rank: 3
Schläfli Type: {14,7}
Vertices, edges, …: 98, 343, 49
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 14
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Quotients maximal quotients in bold

7-fold

{14,7}*196

49-fold

{2,7}*28

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)^2> of order 7

13 facets

7 of {2}*4
6 of {14}*28

14 vertex figures

14 of {7}*14

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.