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

Overview

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

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

4-fold

{6,8}*192a

16-fold

{6,4}*48b

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=<(s0*s1)^2*(s2*s1)^6*s0*s1*s2> of order 2

32 facets

32 of {6}*12

16 vertex figures

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

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

16 facets

16 of {6}*12

12 vertex figures

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

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

16 facets

16 of {6}*12

8 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.