Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,4}

Atlas Canonical Name {12,4}*768a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,90280)
Rank
3
Schläfli Type
{12,4}
Vertices, edges, …
96, 192, 32
Order of s0s1s2
24
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

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

32-fold

48-fold

64-fold

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

16 facets

48 vertex figures

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

18 facets

48 vertex figures

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

16 facets

54 vertex figures

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

16 facets

48 vertex figures

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

8 facets

24 vertex figures

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

8 facets

27 vertex figures

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

8 facets

30 vertex figures

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

8 facets

24 vertex figures

P/N, where N=<(s0*s1)^6, s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1> of order 4

10 facets

24 vertex figures

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

9 facets

24 vertex figures

P/N, where N=<(s1*s2)^2, s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2, (s0*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 8

5 facets

15 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle