Polytope of Type {3,6,33} with group SmallGroup(1188,41)

Overview

Group: SmallGroup(1188,41)
Rank: 4
Schläfli Type: {3,6,33}
Vertices, edges, …: 3, 9, 99, 33
Order of s₀s₁s₂s₃: 33
Order of s₀s₁s₂s₃s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

3-fold

{3,2,33}*396

9-fold

{3,2,11}*132

11-fold

{3,6,3}*108

33-fold

{3,2,3}*36

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(34,67)(35,69)(36,68)(37,70)(38,72)(39,71)(40,73)(41,75)(42,74)(43,76)(44,78)(45,77)(46,79)(47,81)(48,80)(49,82)(50,84)(51,83)(52,85)(53,87)(54,86)(55,88)(56,90)(57,89)(58,91)(59,93)(60,92)(61,94)(62,96)(63,95)(64,97)(65,99)(66,98);;
s1 := ( 1,34)( 2,36)( 3,35)( 4,37)( 5,39)( 6,38)( 7,40)( 8,42)( 9,41)(10,43)(11,45)(12,44)(13,46)(14,48)(15,47)(16,49)(17,51)(18,50)(19,52)(20,54)(21,53)(22,55)(23,57)(24,56)(25,58)(26,60)(27,59)(28,61)(29,63)(30,62)(31,64)(32,66)(33,65)(68,69)(71,72)(74,75)(77,78)(80,81)(83,84)(86,87)(89,90)(92,93)(95,96)(98,99);;
s2 := ( 2, 3)( 4,31)( 5,33)( 6,32)( 7,28)( 8,30)( 9,29)(10,25)(11,27)(12,26)(13,22)(14,24)(15,23)(16,19)(17,21)(18,20)(34,35)(37,65)(38,64)(39,66)(40,62)(41,61)(42,63)(43,59)(44,58)(45,60)(46,56)(47,55)(48,57)(49,53)(50,52)(51,54)(67,69)(70,99)(71,98)(72,97)(73,96)(74,95)(75,94)(76,93)(77,92)(78,91)(79,90)(80,89)(81,88)(82,87)(83,86)(84,85);;
s3 := ( 1, 4)( 2, 6)( 3, 5)( 7,31)( 8,33)( 9,32)(10,28)(11,30)(12,29)(13,25)(14,27)(15,26)(16,22)(17,24)(18,23)(20,21)(34,37)(35,39)(36,38)(40,64)(41,66)(42,65)(43,61)(44,63)(45,62)(46,58)(47,60)(48,59)(49,55)(50,57)(51,56)(53,54)(67,70)(68,72)(69,71)(73,97)(74,99)(75,98)(76,94)(77,96)(78,95)(79,91)(80,93)(81,92)(82,88)(83,90)(84,89)(86,87);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(99)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(34,67)(35,69)(36,68)(37,70)(38,72)(39,71)(40,73)(41,75)(42,74)(43,76)(44,78)(45,77)(46,79)(47,81)(48,80)(49,82)(50,84)(51,83)(52,85)(53,87)(54,86)(55,88)(56,90)(57,89)(58,91)(59,93)(60,92)(61,94)(62,96)(63,95)(64,97)(65,99)(66,98);
s1 := Sym(99)!( 1,34)( 2,36)( 3,35)( 4,37)( 5,39)( 6,38)( 7,40)( 8,42)( 9,41)(10,43)(11,45)(12,44)(13,46)(14,48)(15,47)(16,49)(17,51)(18,50)(19,52)(20,54)(21,53)(22,55)(23,57)(24,56)(25,58)(26,60)(27,59)(28,61)(29,63)(30,62)(31,64)(32,66)(33,65)(68,69)(71,72)(74,75)(77,78)(80,81)(83,84)(86,87)(89,90)(92,93)(95,96)(98,99);
s2 := Sym(99)!( 2, 3)( 4,31)( 5,33)( 6,32)( 7,28)( 8,30)( 9,29)(10,25)(11,27)(12,26)(13,22)(14,24)(15,23)(16,19)(17,21)(18,20)(34,35)(37,65)(38,64)(39,66)(40,62)(41,61)(42,63)(43,59)(44,58)(45,60)(46,56)(47,55)(48,57)(49,53)(50,52)(51,54)(67,69)(70,99)(71,98)(72,97)(73,96)(74,95)(75,94)(76,93)(77,92)(78,91)(79,90)(80,89)(81,88)(82,87)(83,86)(84,85);
s3 := Sym(99)!( 1, 4)( 2, 6)( 3, 5)( 7,31)( 8,33)( 9,32)(10,28)(11,30)(12,29)(13,25)(14,27)(15,26)(16,22)(17,24)(18,23)(20,21)(34,37)(35,39)(36,38)(40,64)(41,66)(42,65)(43,61)(44,63)(45,62)(46,58)(47,60)(48,59)(49,55)(50,57)(51,56)(53,54)(67,70)(68,72)(69,71)(73,97)(74,99)(75,98)(76,94)(77,96)(78,95)(79,91)(80,93)(81,92)(82,88)(83,90)(84,89)(86,87);
poly := sub<Sym(99)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References