Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,24}

Atlas Canonical Name {6,24}*960d

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Overview

Group
SmallGroup(960,5719)
Rank
3
Schläfli Type
{6,24}
Vertices, edges, …
20, 240, 80
Order of s0s1s2
24
Order of s0s1s2s1
20
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

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