Polytope of Type {8,6} with group SmallGroup(768,1086052)

Overview

Group: SmallGroup(768,1086052)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 64, 192, 48
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{8,6}*384b

4-fold

{4,6}*192a

16-fold

{4,6}*48c

32-fold

{4,3}*24

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*s2*(s1*s0)^3*s1*s2> of order 2

36 facets

12 of {8}*16
24 of {4}*8

32 vertex figures

32 of {6}*12

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

24 facets

24 of {8}*16

36 vertex figures

28 of {6}*12
8 of {3}*6

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

16 facets

16 of {8}*16

24 vertex figures

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

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

20 facets

6 of {8}*16
10 of {4}*8
4 of {2}*4

16 vertex figures

16 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 8

12 facets

3 of {8}*16
3 of {4}*8
6 of {2}*4

8 vertex figures

8 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,55)( 6,56)( 7,53)( 8,54)( 9,60)(10,59)(11,58)(12,57)(13,62)(14,61)(15,64)(16,63)(17,33)(18,34)(19,35)(20,36)(21,39)(22,40)(23,37)(24,38)(25,44)(26,43)(27,42)(28,41)(29,46)(30,45)(31,48)(32,47);;
s1 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,10)(11,12)(17,19)(18,20)(21,24)(22,23)(25,32)(26,31)(27,30)(28,29)(33,60)(34,59)(35,58)(36,57)(37,63)(38,64)(39,61)(40,62)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49);;
s2 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,33)(18,34)(19,36)(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,46)(30,45)(31,47)(32,48)(51,52)(53,58)(54,57)(55,59)(56,60)(61,62);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(64)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,55)( 6,56)( 7,53)( 8,54)( 9,60)(10,59)(11,58)(12,57)(13,62)(14,61)(15,64)(16,63)(17,33)(18,34)(19,35)(20,36)(21,39)(22,40)(23,37)(24,38)(25,44)(26,43)(27,42)(28,41)(29,46)(30,45)(31,48)(32,47);
s1 := Sym(64)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,10)(11,12)(17,19)(18,20)(21,24)(22,23)(25,32)(26,31)(27,30)(28,29)(33,60)(34,59)(35,58)(36,57)(37,63)(38,64)(39,61)(40,62)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49);
s2 := Sym(64)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,33)(18,34)(19,36)(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,46)(30,45)(31,47)(32,48)(51,52)(53,58)(54,57)(55,59)(56,60)(61,62);
poly := sub<Sym(64)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 >;

References

None.

to this polytope.