Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,4}

Atlas Canonical Name {14,4}*784

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(784,165)
Rank
3
Schläfli Type
{14,4}
Vertices, edges, …
98, 196, 28
Order of s0s1s2
4
Order of s0s1s2s1
14
Also known as
{14,4}4. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

49-fold

98-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s2*(s1*s0)^6*s1*s2> of order 2

15 facets

49 vertex figures

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

4 facets

14 vertex figures

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

4 facets

14 vertex figures

P/N, where N=<s0*s2*s1*s0*s1*s2> of order 7

16 facets

14 vertex figures

P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1)^7> of order 14

9 facets

7 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1,50)( 2,56)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,92)( 9,98)(10,97)(11,96)(12,95)(13,94)(14,93)(15,85)(16,91)(17,90)(18,89)(19,88)(20,87)(21,86)(22,78)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,71)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,64)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,57)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58);;
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)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63)(64,92)(65,93)(66,94)(67,95)(68,96)(69,97)(70,98)(71,85)(72,86)(73,87)(74,88)(75,89)(76,90)(77,91);;
s2 := ( 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)(51,57)(52,64)(53,71)(54,78)(55,85)(56,92)(59,65)(60,72)(61,79)(62,86)(63,93)(67,73)(68,80)(69,87)(70,94)(75,81)(76,88)(77,95)(83,89)(84,96)(91,97);;
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, 
s2*s0*s1*s2*s0*s1*s2*s0*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(98)!( 1,50)( 2,56)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,92)( 9,98)(10,97)(11,96)(12,95)(13,94)(14,93)(15,85)(16,91)(17,90)(18,89)(19,88)(20,87)(21,86)(22,78)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,71)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,64)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,57)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58);
s1 := Sym(98)!( 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)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63)(64,92)(65,93)(66,94)(67,95)(68,96)(69,97)(70,98)(71,85)(72,86)(73,87)(74,88)(75,89)(76,90)(77,91);
s2 := Sym(98)!( 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)(51,57)(52,64)(53,71)(54,78)(55,85)(56,92)(59,65)(60,72)(61,79)(62,86)(63,93)(67,73)(68,80)(69,87)(70,94)(75,81)(76,88)(77,95)(83,89)(84,96)(91,97);
poly := sub<Sym(98)|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, 
s2*s0*s1*s2*s0*s1*s2*s0*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*s0*s1 >;

References

None.

to this polytope.

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