Polytope of Type {8,48} with group SmallGroup(768,82962)

Overview

Group: SmallGroup(768,82962)
Rank: 3
Schläfli Type: {8,48}
Vertices, edges, …: 8, 192, 48
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

{8,24}*384d

3-fold

{8,16}*256a

4-fold

6-fold

{8,8}*128c

8-fold

12-fold

16-fold

24-fold

32-fold

{2,6}*24

48-fold

64-fold

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

Permutation Representation (Magma)

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

References