Polytope of Type {8,12} with group SmallGroup(1920,240800)

Overview

Group: SmallGroup(1920,240800)
Rank: 3
Schläfli Type: {8,12}
Vertices, edges, …: 80, 480, 120
Order of s₀s₁s₂: 20
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=<s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^3> of order 2

60 facets

60 of {8}*16

40 vertex figures

40 of {12}*24

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

40 facets

40 of {8}*16

32 vertex figures

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

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^3*s2*s1*s2> of order 6

20 facets

20 of {8}*16

16 vertex figures

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

Representations

Permutation Representation (GAP)

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