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

Overview

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

{4,6}*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*s2*s1)^5> of order 2

60 facets

60 of {8}*16

40 vertex figures

40 of {12}*24

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

60 facets

60 of {8}*16

40 vertex figures

40 of {12}*24

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

40 facets

40 of {8}*16

32 vertex figures

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

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

References

None.

to this polytope.