Polytope of Type {20,12} with group SmallGroup(1920,240800)

Overview

Group: SmallGroup(1920,240800)
Rank: 3
Schläfli Type: {20,12}
Vertices, edges, …: 80, 480, 48
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 8
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

{5,6}*120a

120-fold

{2,4}*16

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

Permutation Representation (Magma)

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

References