Polytope of Type {8,6} with group SmallGroup(768,1086051)

Overview

Group: SmallGroup(768,1086051)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 64, 192, 48
Order of s₀s₁s₂: 6
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

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*s1)^4> of order 2

32 facets

16 of {4}*8
16 of {8}*16

32 vertex figures

32 of {6}*12

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

16 facets

8 of {4}*8
8 of {8}*16

16 vertex figures

16 of {6}*12

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

18 facets

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

16 vertex figures

16 of {6}*12

P/N, where N=<(s0*s1)^2, s0*(s2*s1)^2*s0*s1*s0*s2*s1*s2> of order 8

10 facets

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

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

References

None.

to this polytope.