Polytope of Type {4,6} with group SmallGroup(1920,240864)

Overview

Group: SmallGroup(1920,240864)
Rank: 3
Schläfli Type: {4,6}
Vertices, edges, …: 160, 480, 240
Order of s₀s₁s₂: 40
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

{4,6}*960

4-fold

{4,6}*480

8-fold

16-fold

{4,6}*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=<s1*s0*(s2*s1*s0*s1)^3*s2*s1> of order 2

124 facets

116 of {4}*8
8 of {2}*4

80 vertex figures

80 of {6}*12

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

120 facets

120 of {4}*8

82 vertex figures

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

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

80 facets

80 of {4}*8

64 vertex figures

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

P/N, where N=<s1*s0*(s2*s1*s0*s1)^3*s2*s1, s1*(s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 4

62 facets

58 of {4}*8
4 of {2}*4

40 vertex figures

40 of {6}*12

P/N, where N=<(s0*s2*s1)^3*s0*(s2*s1)^2, s1*s0*(s2*s1*s0*s1)^3*s2*s1> of order 4

62 facets

58 of {4}*8
4 of {2}*4

42 vertex figures

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

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

48 facets

48 of {4}*8

32 vertex figures

32 of {6}*12

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

44 facets

8 of {2}*4
36 of {4}*8

32 vertex figures

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

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

40 facets

40 of {4}*8

34 vertex figures

22 of {6}*12
4 of {3}*6
8 of {2}*4

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1*s0*s1> of order 10

28 facets

20 of {4}*8
8 of {2}*4

16 vertex figures

16 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*(s1*s2)^3> of order 20

14 facets

10 of {4}*8
4 of {2}*4

8 vertex figures

8 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1,76)( 2,87)( 3,57)( 4,91)( 5,92)( 6,77)( 7,94)( 8,53)( 9,88)(10,70)(11,54)(12,62)(13,50)(14,93)(15,52)(16,75)(17,55)(18,60)(19,86)(20,84)(21,72)(22,58)(23,49)(24,69)(25,59)(26,96)(27,64)(28,89)(29,73)(30,65)(31,61)(32,63)(33,74)(34,67)(35,82)(36,68)(37,51)(38,83)(39,79)(40,85)(41,71)(42,81)(43,80)(44,95)(45,66)(46,78)(47,56)(48,90);;
s1 := ( 1,49)( 2,50)( 3,64)( 4,52)( 5,53)( 6,54)( 7,55)( 8,72)( 9,57)(10,74)(11,58)(12,68)(13,75)(14,62)(15,84)(16,86)(17,69)(18,60)(19,87)(20,67)(21,81)(22,90)(23,70)(24,96)(25,59)(26,94)(27,82)(28,78)(29,95)(30,65)(31,61)(32,63)(33,76)(34,91)(35,88)(36,83)(37,51)(38,93)(39,66)(40,80)(41,71)(42,92)(43,79)(44,89)(45,85)(46,73)(47,56)(48,77);;
s2 := ( 1,18)( 2,25)( 3,21)( 4,30)( 5,31)( 6,32)( 7,37)( 8,20)( 9,41)(10,15)(11,27)(12,22)(13,24)(14,47)(16,23)(17,36)(19,28)(26,39)(29,35)(33,43)(34,44)(38,46)(40,42)(45,48)(49,75)(50,69)(51,94)(52,70)(53,84)(54,64)(55,68)(56,93)(57,72)(58,62)(59,87)(60,76)(61,92)(63,77)(65,91)(66,90)(67,95)(71,88)(73,82)(74,80)(78,83)(79,96)(81,85)(86,89);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(96)!( 1,76)( 2,87)( 3,57)( 4,91)( 5,92)( 6,77)( 7,94)( 8,53)( 9,88)(10,70)(11,54)(12,62)(13,50)(14,93)(15,52)(16,75)(17,55)(18,60)(19,86)(20,84)(21,72)(22,58)(23,49)(24,69)(25,59)(26,96)(27,64)(28,89)(29,73)(30,65)(31,61)(32,63)(33,74)(34,67)(35,82)(36,68)(37,51)(38,83)(39,79)(40,85)(41,71)(42,81)(43,80)(44,95)(45,66)(46,78)(47,56)(48,90);
s1 := Sym(96)!( 1,49)( 2,50)( 3,64)( 4,52)( 5,53)( 6,54)( 7,55)( 8,72)( 9,57)(10,74)(11,58)(12,68)(13,75)(14,62)(15,84)(16,86)(17,69)(18,60)(19,87)(20,67)(21,81)(22,90)(23,70)(24,96)(25,59)(26,94)(27,82)(28,78)(29,95)(30,65)(31,61)(32,63)(33,76)(34,91)(35,88)(36,83)(37,51)(38,93)(39,66)(40,80)(41,71)(42,92)(43,79)(44,89)(45,85)(46,73)(47,56)(48,77);
s2 := Sym(96)!( 1,18)( 2,25)( 3,21)( 4,30)( 5,31)( 6,32)( 7,37)( 8,20)( 9,41)(10,15)(11,27)(12,22)(13,24)(14,47)(16,23)(17,36)(19,28)(26,39)(29,35)(33,43)(34,44)(38,46)(40,42)(45,48)(49,75)(50,69)(51,94)(52,70)(53,84)(54,64)(55,68)(56,93)(57,72)(58,62)(59,87)(60,76)(61,92)(63,77)(65,91)(66,90)(67,95)(71,88)(73,82)(74,80)(78,83)(79,96)(81,85)(86,89);
poly := sub<Sym(96)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

References

None.

to this polytope.