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

Overview

Group: SmallGroup(384,11319)
Rank: 4
Schläfli Type: {2,8,12}
Vertices, edges, …: 2, 8, 48, 12
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

{2,8,12,2} ·768

Vertex figure of

Quotients maximal quotients in bold

2-fold

3-fold

{2,8,4}*128a

4-fold

6-fold

8-fold

{2,2,6}*48

12-fold

16-fold

{2,2,3}*24

24-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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