Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,6}

Atlas Canonical Name {10,6}*1920b

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Overview

Group
SmallGroup(1920,240997)
Rank
3
Schläfli Type
{10,6}
Vertices, edges, …
160, 480, 96
Order of s0s1s2
10
Order of s0s1s2s1
5
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

2-fold

32-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

48 facets

80 vertex figures

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

48 facets

80 vertex figures

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

48 facets

88 vertex figures

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

32 facets

56 vertex figures

P/N, where N=<(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4

24 facets

48 vertex figures

P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, (s0*(s1*s2)^2*s1)^2> of order 4

24 facets

44 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 3, 5)( 4, 7)( 6, 9)( 8,10);;
s1 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := ( 3, 9)( 4,10)( 5, 6)( 7, 8);;
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*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(10)!( 3, 5)( 4, 7)( 6, 9)( 8,10);
s1 := Sym(10)!( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(10)!( 3, 9)( 4,10)( 5, 6)( 7, 8);
poly := sub<Sym(10)|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*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.

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