Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,4}

Atlas Canonical Name {24,4}*192a

▶ Play as a twisty puzzle

Overview

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

Special Properties

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

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

References

None.

to this polytope.

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