Polytope of Type {12,6} with group SmallGroup(768,1086052)

Overview

Group: SmallGroup(768,1086052)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 64, 192, 32
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 3
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,6}*384a

4-fold

{6,6}*192a

32-fold

{3,3}*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*s0*s2)^3*s1*s2> of order 2

16 facets

16 of {12}*24

32 vertex figures

32 of {6}*12

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

References

None.

to this polytope.