Polytope of Type {12,6} with group SmallGroup(960,10877)

Overview

Group: SmallGroup(960,10877)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 80, 240, 40
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,6}*480

4-fold

8-fold

{6,6}*120

120-fold

{2,2}*8

Covers minimal covers in bold

2-fold

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*(s2*s1)^2*s0*s2*s1*s2> of order 2

20 facets

20 of {12}*24

40 vertex figures

40 of {6}*12

P/N, where N=<s1*s0*s1*s2*(s1*s0)^3*s1*s2> of order 5

8 facets

8 of {12}*24

16 vertex figures

16 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.