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

Overview

Group: SmallGroup(768,1086052)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 48, 192, 64
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

{6,8}*384b

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*s2)^4> of order 2

32 facets

32 of {6}*12

36 vertex figures

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

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

36 facets

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

24 vertex figures

24 of {8}*16

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

24 facets

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

16 vertex figures

16 of {8}*16

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

16 facets

16 of {6}*12

20 vertex figures

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

P/N, where N=<(s1*s2)^4, (s0*s1)^2*(s2*s1*s0)^2, s0*(s1*s2)^3*s1*s0*s1*s2*s1> of order 8

8 facets

8 of {6}*12

12 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.