Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12}

Atlas Canonical Name {4,12}*768a

▶ Play as a twisty puzzle

Overview

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

48 facets

16 vertex figures

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

48 facets

18 vertex figures

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

54 facets

16 vertex figures

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

48 facets

16 vertex figures

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

24 facets

8 vertex figures

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

27 facets

8 vertex figures

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

30 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

10 vertex figures

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

24 facets

9 vertex figures

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

15 facets

5 vertex figures

Representations

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

References

None.

to this polytope.

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