Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,14}

Atlas Canonical Name {8,14}*784b

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Overview

Group
SmallGroup(784,161)
Rank
3
Schläfli Type
{8,14}
Vertices, edges, …
28, 196, 49
Order of s0s1s2
8
Order of s0s1s2s1
14
Also known as
if this polytope has a 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

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle