Polytope of Type {4,14} with group SmallGroup(392,37)

Overview

Group: SmallGroup(392,37)
Rank: 3
Schläfli Type: {4,14}
Vertices, edges, …: 14, 98, 49
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 14
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

{4,14}*784

3-fold

{12,14}*1176

4-fold

5-fold

{20,14}*1960

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References