Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,12}

Atlas Canonical Name {12,12}*1920a

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Overview

Group
SmallGroup(1920,240507)
Rank
3
Schläfli Type
{12,12}
Vertices, edges, …
80, 480, 80
Order of s0s1s2
12
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Self-Dual
  • Self-Petrie

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)^4*(s0*(s2*s1)^2)^2*s2> of order 2

40 facets

40 vertex figures

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

40 facets

40 vertex figures

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

40 facets

40 vertex figures

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

40 facets

40 vertex figures

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

40 facets

40 vertex figures

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

40 facets

40 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

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

20 facets

20 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 5

16 facets

16 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 4, 5)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);;
s1 := ( 1, 2)( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,32)(15,33)(16,30)(17,31)(18,37)(19,36)(20,35)(21,34);;
s2 := ( 2, 4)( 3, 5)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37);;
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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(37)!( 2, 3)( 4, 5)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
s1 := Sym(37)!( 1, 2)( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,32)(15,33)(16,30)(17,31)(18,37)(19,36)(20,35)(21,34);
s2 := Sym(37)!( 2, 4)( 3, 5)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37);
poly := sub<Sym(37)|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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.

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