Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,24}

Atlas Canonical Name {4,24}*1920a

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Overview

Group
SmallGroup(1920,240560)
Rank
3
Schläfli Type
{4,24}
Vertices, edges, …
40, 480, 240
Order of s0s1s2
40
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=<(s1*s0*s1*s2)^3> of order 2

120 facets

20 vertex figures

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

120 facets

20 vertex figures

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

128 facets

20 vertex figures

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

120 facets

20 vertex figures

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

80 facets

16 vertex figures

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

72 facets

10 vertex figures

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

64 facets

10 vertex figures

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

48 facets

8 vertex figures

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

40 facets

8 vertex figures

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

40 facets

8 vertex figures

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

24 facets

6 vertex figures

Representations

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

References

None.

to this polytope.

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