Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,4}

Atlas Canonical Name {12,4}*384d

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Overview

Group
SmallGroup(384,17873)
Rank
3
Schläfli Type
{12,4}
Vertices, edges, …
48, 96, 16
Order of s0s1s2
12
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

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

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

12-fold

16-fold

24-fold

32-fold

48-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

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

8 facets

24 vertex figures

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

8 facets

24 vertex figures

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

8 facets

32 vertex figures

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

8 facets

24 vertex figures

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

8 facets

24 vertex figures

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

8 facets

16 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1> of order 4

4 facets

20 vertex figures

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

4 facets

12 vertex figures

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

4 facets

12 vertex figures

Representations

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

References

None.

to this polytope.

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