Polytope of Type {24,16} with group SmallGroup(768,82983)

Overview

Group: SmallGroup(768,82983)
Rank: 3
Schläfli Type: {24,16}
Vertices, edges, …: 24, 192, 16
Order of s₀s₁s₂: 48
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{24,8}*384a

3-fold

{8,16}*256b

4-fold

6-fold

{8,8}*128c

8-fold

12-fold

16-fold

24-fold

32-fold

{6,2}*24

48-fold

64-fold

{3,2}*12

96-fold

{2,2}*8

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)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,58)( 8,60)( 9,59)(10,55)(11,57)(12,56)(13,67)(14,69)(15,68)(16,70)(17,72)(18,71)(19,61)(20,63)(21,62)(22,64)(23,66)(24,65)(25,73)(26,75)(27,74)(28,76)(29,78)(30,77)(31,82)(32,84)(33,83)(34,79)(35,81)(36,80)(37,91)(38,93)(39,92)(40,94)(41,96)(42,95)(43,85)(44,87)(45,86)(46,88)(47,90)(48,89);;
s1 := ( 1, 3)( 4, 6)( 7,12)( 8,11)( 9,10)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(25,39)(26,38)(27,37)(28,42)(29,41)(30,40)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(49,51)(52,54)(55,60)(56,59)(57,58)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)(73,87)(74,86)(75,85)(76,90)(77,89)(78,88)(79,96)(80,95)(81,94)(82,93)(83,92)(84,91);;
s2 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,31)(11,32)(12,33)(13,46)(14,47)(15,48)(16,43)(17,44)(18,45)(19,40)(20,41)(21,42)(22,37)(23,38)(24,39)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,82)(56,83)(57,84)(58,79)(59,80)(60,81)(61,94)(62,95)(63,96)(64,91)(65,92)(66,93)(67,88)(68,89)(69,90)(70,85)(71,86)(72,87);;
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*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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*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(96)!( 1,49)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,58)( 8,60)( 9,59)(10,55)(11,57)(12,56)(13,67)(14,69)(15,68)(16,70)(17,72)(18,71)(19,61)(20,63)(21,62)(22,64)(23,66)(24,65)(25,73)(26,75)(27,74)(28,76)(29,78)(30,77)(31,82)(32,84)(33,83)(34,79)(35,81)(36,80)(37,91)(38,93)(39,92)(40,94)(41,96)(42,95)(43,85)(44,87)(45,86)(46,88)(47,90)(48,89);
s1 := Sym(96)!( 1, 3)( 4, 6)( 7,12)( 8,11)( 9,10)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(25,39)(26,38)(27,37)(28,42)(29,41)(30,40)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(49,51)(52,54)(55,60)(56,59)(57,58)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)(73,87)(74,86)(75,85)(76,90)(77,89)(78,88)(79,96)(80,95)(81,94)(82,93)(83,92)(84,91);
s2 := Sym(96)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,31)(11,32)(12,33)(13,46)(14,47)(15,48)(16,43)(17,44)(18,45)(19,40)(20,41)(21,42)(22,37)(23,38)(24,39)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,82)(56,83)(57,84)(58,79)(59,80)(60,81)(61,94)(62,95)(63,96)(64,91)(65,92)(66,93)(67,88)(68,89)(69,90)(70,85)(71,86)(72,87);
poly := sub<Sym(96)|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*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References