Polytope of Type {12,8} with group SmallGroup(1920,240800)

Overview

Group: SmallGroup(1920,240800)
Rank: 3
Schläfli Type: {12,8}
Vertices, edges, …: 120, 480, 80
Order of s₀s₁s₂: 20
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-fold

8-fold

16-fold

{6,4}*120

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

40 facets

40 of {12}*24

60 vertex figures

60 of {8}*16

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

32 facets

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

40 vertex figures

40 of {8}*16

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

16 facets

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

20 vertex figures

20 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.