Polytope of Type {20,8} with group SmallGroup(1920,240838)

Overview

Group: SmallGroup(1920,240838)
Rank: 3
Schläfli Type: {20,8}
Vertices, edges, …: 120, 480, 48
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 6
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

{10,4}*480c

8-fold

16-fold

{5,4}*120

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References