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

Overview

Group: SmallGroup(768,1086051)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 48, 192, 64
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
Self-Petrie

Quotients maximal quotients in bold

4-fold

{6,4}*192a

16-fold

{6,4}*48c

32-fold

{3,4}*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=<s1*s0*(s1*s2)^3*s1*s0*s2*s1> of order 2

32 facets

32 of {6}*12

32 vertex figures

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

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

16 facets

16 of {6}*12

16 vertex figures

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

P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 4

16 facets

16 of {6}*12

18 vertex figures

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

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

8 facets

8 of {6}*12

10 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.