Polytope of Type {4,10} with group SmallGroup(1920,240816)

Overview

Group: SmallGroup(1920,240816)
Rank: 3
Schläfli Type: {4,10}
Vertices, edges, …: 96, 480, 240
Order of s₀s₁s₂: 24
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

{4,10}*960

4-fold

8-fold

16-fold

{4,5}*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=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2> of order 2

120 facets

120 of {4}*8

48 vertex figures

48 of {10}*20

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

120 facets

120 of {4}*8

60 vertex figures

24 of {5}*10
36 of {10}*20

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

124 facets

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

48 vertex figures

48 of {10}*20

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

80 facets

80 of {4}*8

32 vertex figures

32 of {10}*20

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

48 facets

48 of {4}*8

32 vertex figures

16 of {10}*20
16 of {2}*4

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

44 facets

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

16 vertex figures

16 of {10}*20

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

28 facets

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

16 vertex figures

8 of {10}*20
8 of {2}*4

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.