Polytope of Type {8,12,2} with group SmallGroup(384,11319)

Overview

Group: SmallGroup(384,11319)
Rank: 4
Schläfli Type: {8,12,2}
Vertices, edges, …: 8, 48, 12, 2
Order of s₀s₁s₂s₃: 24
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

{2,8,12,2} ·768

Quotients maximal quotients in bold

2-fold

3-fold

{8,4,2}*128a

4-fold

6-fold

8-fold

{2,6,2}*48

12-fold

16-fold

{2,3,2}*24

24-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

5-fold

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

Permutation Representation (Magma)

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