Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,24}

Atlas Canonical Name {6,24}*1152e

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,155791)
Rank
3
Schläfli Type
{6,24}
Vertices, edges, …
24, 288, 96
Order of s0s1s2
6
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

48-fold

96-fold

144-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*s0*s2)^2*(s1*s0)^2*s2*s1*s0*s2*s1> of order 2

48 facets

16 vertex figures

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

48 facets

12 vertex figures

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

48 facets

12 vertex figures

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

24 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

12 vertex figures

Representations

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

References

None.

to this polytope.

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