Polytope of Type {12,6} with group SmallGroup(288,1028)

Overview

Group: SmallGroup(288,1028)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 24, 72, 12
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{12,6}*144d

3-fold

{4,6}*96

4-fold

{6,6}*72a

6-fold

12-fold

24-fold

36-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-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*s0*s1*s2)^2> of order 2

8 facets

4 of {12}*24
4 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2

6 facets

6 of {12}*24

12 vertex figures

12 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1, 2)( 3, 4)( 5,10)( 6, 9)( 7,12)( 8,11)(13,14)(15,16)(17,22)(18,21)(19,24)(20,23)(25,26)(27,28)(29,34)(30,33)(31,36)(32,35)(37,38)(39,40)(41,46)(42,45)(43,48)(44,47)(49,50)(51,52)(53,58)(54,57)(55,60)(56,59)(61,62)(63,64)(65,70)(66,69)(67,72)(68,71);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(37,41)(38,43)(39,42)(40,44)(46,47)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)(59,70)(60,72);;
s2 := ( 1,49)( 2,50)( 3,52)( 4,51)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)(11,60)(12,59)(13,37)(14,38)(15,40)(16,39)(17,41)(18,42)(19,44)(20,43)(21,45)(22,46)(23,48)(24,47)(25,61)(26,62)(27,64)(28,63)(29,65)(30,66)(31,68)(32,67)(33,69)(34,70)(35,72)(36,71);;
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*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(72)!( 1, 2)( 3, 4)( 5,10)( 6, 9)( 7,12)( 8,11)(13,14)(15,16)(17,22)(18,21)(19,24)(20,23)(25,26)(27,28)(29,34)(30,33)(31,36)(32,35)(37,38)(39,40)(41,46)(42,45)(43,48)(44,47)(49,50)(51,52)(53,58)(54,57)(55,60)(56,59)(61,62)(63,64)(65,70)(66,69)(67,72)(68,71);
s1 := Sym(72)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(37,41)(38,43)(39,42)(40,44)(46,47)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)(59,70)(60,72);
s2 := Sym(72)!( 1,49)( 2,50)( 3,52)( 4,51)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)(11,60)(12,59)(13,37)(14,38)(15,40)(16,39)(17,41)(18,42)(19,44)(20,43)(21,45)(22,46)(23,48)(24,47)(25,61)(26,62)(27,64)(28,63)(29,65)(30,66)(31,68)(32,67)(33,69)(34,70)(35,72)(36,71);
poly := sub<Sym(72)|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*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.