Polytope of Type {12,6} with group SmallGroup(1920,240800)

Overview

Group: SmallGroup(1920,240800)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 160, 480, 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-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

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

32 facets

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

64 vertex figures

48 of {6}*12
16 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 {12}*24

32 vertex figures

32 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.