Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,24}

Atlas Canonical Name {4,24}*192a

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Overview

Group
SmallGroup(192,291)
Rank
3
Schläfli Type
{4,24}
Vertices, edges, …
4, 48, 24
Order of s0s1s2
24
Order of s0s1s2s1
2
Also known as
{4,24|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)(21,47)(22,43)(23,45)(24,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)(60,83)(61,88)(62,90)(63,89)(64,85)(65,87)(66,86)(67,94)(68,96)(69,95)(70,91)(71,93)(72,92);;
s2 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,17)(14,16)(15,18)(19,23)(20,22)(21,24)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(49,50)(52,53)(55,56)(58,59)(61,65)(62,64)(63,66)(67,71)(68,70)(69,72)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(96)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);
s1 := Sym(96)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)(21,47)(22,43)(23,45)(24,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)(60,83)(61,88)(62,90)(63,89)(64,85)(65,87)(66,86)(67,94)(68,96)(69,95)(70,91)(71,93)(72,92);
s2 := Sym(96)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,17)(14,16)(15,18)(19,23)(20,22)(21,24)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(49,50)(52,53)(55,56)(58,59)(61,65)(62,64)(63,66)(67,71)(68,70)(69,72)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96);
poly := sub<Sym(96)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

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