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

Overview

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

{8,6}*384b

4-fold

{4,6}*192a

16-fold

{4,6}*48c

32-fold

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

Permutation Representation (Magma)

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

References