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

Overview

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

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

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)^3> of order 2

42 facets

4 of {3}*6
38 of {6}*12

40 vertex figures

40 of {6}*12

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

40 facets

40 of {6}*12

42 vertex figures

38 of {6}*12
4 of {3}*6

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

32 facets

8 of {2}*4
24 of {6}*12

32 vertex figures

24 of {6}*12
8 of {2}*4

P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1> of order 5

16 facets

16 of {6}*12

16 vertex figures

16 of {6}*12

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

18 facets

4 of {3}*6
4 of {2}*4
10 of {6}*12

16 vertex figures

12 of {6}*12
4 of {2}*4

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

16 facets

4 of {2}*4
12 of {6}*12

18 vertex figures

10 of {6}*12
4 of {3}*6
4 of {2}*4

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

References

None.

to this polytope.