Polytope of Type {16,6} with group SmallGroup(768,1085833)

Overview

Group: SmallGroup(768,1085833)
Rank: 3
Schläfli Type: {16,6}
Vertices, edges, …: 64, 192, 24
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 16
Also known as: {16,6}₃. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

4-fold

{8,6}*192a

16-fold

{4,6}*48b

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)^8> of order 2

16 facets

8 of {8}*16
8 of {16}*32

32 vertex figures

32 of {6}*12

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

8 facets

4 of {8}*16
4 of {16}*32

16 vertex figures

16 of {6}*12

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

12 facets

8 of {4}*8
4 of {16}*32

16 vertex figures

16 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.