Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,6}

Atlas Canonical Name {14,6}*588

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Overview

Group
SmallGroup(588,35)
Rank
3
Schläfli Type
{14,6}
Vertices, edges, …
49, 147, 21
Order of s0s1s2
3
Order of s0s1s2s1
14
Also known as
{14,6}3. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

None.

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

References

None.

to this polytope.

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