Polytope of Type {12,8} with group SmallGroup(1920,240798)

Overview

Group: SmallGroup(1920,240798)
Rank: 3
Schläfli Type: {12,8}
Vertices, edges, …: 120, 480, 80
Order of s₀s₁s₂: 10
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

{6,4}*120

240-fold

{2,2}*8

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

40 facets

40 of {12}*24

60 vertex figures

60 of {8}*16

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

40 facets

40 of {12}*24

60 vertex figures

60 of {8}*16

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

32 facets

24 of {12}*24
8 of {4}*8

40 vertex figures

40 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.