Polytope of Type {12,4} with group SmallGroup(192,1470)

Overview

Group: SmallGroup(192,1470)
Rank: 3
Schläfli Type: {12,4}
Vertices, edges, …: 24, 48, 8
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

12-fold

{4,2}*16

16-fold

{3,2}*12

24-fold

{2,2}*8

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

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^2> of order 2

4 facets

4 of {12}*24

16 vertex figures

8 of {2}*4
8 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.