Polytope of Type {12,8} with group SmallGroup(768,1086052)

Overview

Group: SmallGroup(768,1086052)
Rank: 3
Schläfli Type: {12,8}
Vertices, edges, …: 48, 192, 32
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

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

None.

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

References