Polytope of Type {4,6,4} with group SmallGroup(192,1149)

Overview

Group: SmallGroup(192,1149)
Rank: 4
Schläfli Type: {4,6,4}
Vertices, edges, …: 4, 12, 12, 4
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{4,6|2},{6,4|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat
Self-Dual

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

3-fold

{4,2,4}*64

4-fold

{2,6,2}*48

6-fold

8-fold

{2,3,2}*24

12-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

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

Permutation Representation (Magma)

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

References

None.

to this polytope.