Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12}

Atlas Canonical Name {4,12}*1920b

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Overview

Group
SmallGroup(1920,240857)
Rank
3
Schläfli Type
{4,12}
Vertices, edges, …
80, 480, 240
Order of s0s1s2
40
Order of s0s1s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

120-fold

240-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*(s2*s1)^4*s2> of order 3

80 facets

32 vertex figures

P/N, where N=<(s1*s0*s2)^3*s1*s0*(s2*s1)^2*s2> of order 5

48 facets

16 vertex figures

Representations

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

References

None.

to this polytope.

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