Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,14}

Atlas Canonical Name {3,14}*588

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(588,35)
Rank
3
Schläfli Type
{3,14}
Vertices, edges, …
21, 147, 98
Order of s0s1s2
6
Order of s0s1s2s1
14
Also known as
{3,14}6. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

49-fold

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

14 facets

3 vertex figures

P/N, where N=<s0*(s1*s2)^3*s1*s0*(s2*s1)^2*s2> of order 7

14 facets

3 vertex figures

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

14 facets

9 vertex figures

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

References

None.

to this polytope.

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