Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,8}

Atlas Canonical Name {10,8}*1920a

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Overview

Group
SmallGroup(1920,240558)
Rank
3
Schläfli Type
{10,8}
Vertices, edges, …
120, 480, 96
Order of s0s1s2
24
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

60-fold

120-fold

240-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)^3*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2

48 facets

60 vertex figures

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

48 facets

60 vertex figures

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

48 facets

60 vertex figures

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

32 facets

40 vertex figures

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

24 facets

30 vertex figures

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

24 facets

30 vertex figures

P/N, where N=<s0*s2*s1*s0*s1*s2> of order 5

32 facets

24 vertex figures

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

16 facets

20 vertex figures

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

16 facets

20 vertex figures

P/N, where N=<s0*s2*s1*s0*s1*s2, (s1*s0)^3*s2*s1*s0*(s2*s1)^2*s2> of order 10

16 facets

12 vertex figures

P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 10

16 facets

12 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 12

8 facets

10 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(18,21)(19,20);;
s1 := ( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11)(17,20)(19,21);;
s2 := ( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(19,20);;
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*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*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*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(21)!( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(18,21)(19,20);
s1 := Sym(21)!( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11)(17,20)(19,21);
s2 := Sym(21)!( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(19,20);
poly := sub<Sym(21)|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*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*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*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.

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