Polytope of Type {12,8} with group SmallGroup(1920,240838)

Overview

Group: SmallGroup(1920,240838)
Rank: 3
Schläfli Type: {12,8}
Vertices, edges, …: 120, 480, 80
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

{6,4}*480

8-fold

16-fold

{6,4}*120

120-fold

{4,2}*16

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