Polytope of Type {12,3} with group SmallGroup(96,193)

Overview

Group: SmallGroup(96,193)
Rank: 3
Schläfli Type: {12,3}
Vertices, edges, …: 16, 24, 4
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 12
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

{6,3}*48

4-fold

{3,3}*24

Covers minimal covers in bold

2-fold

{12,6}*192b

3-fold

{12,3}*288

4-fold

5-fold

{12,15}*480

6-fold

7-fold

{12,21}*672

8-fold

9-fold

10-fold

11-fold

{12,33}*1056

12-fold

13-fold

{12,39}*1248

14-fold

15-fold

{12,15}*1440c

17-fold

{12,51}*1632

18-fold

19-fold

{12,57}*1824

20-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)(39,40);;
s1 := ( 1, 9)( 2, 4)( 3,25)( 5,10)( 6,48)( 7,47)( 8,13)(11,42)(12,41)(14,26)(15,46)(16,44)(17,36)(18,33)(19,32)(20,34)(21,30)(22,35)(23,31)(24,29)(27,40)(28,39)(37,43)(38,45);;
s2 := ( 1,46)( 2,40)( 3,39)( 4,36)( 5,48)( 6,11)( 7,12)( 8,44)( 9,24)(10,42)(13,21)(14,41)(15,29)(16,30)(17,27)(18,28)(19,31)(20,45)(22,34)(23,43)(25,33)(26,47)(32,37)(35,38);;
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, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(48)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)(39,40);
s1 := Sym(48)!( 1, 9)( 2, 4)( 3,25)( 5,10)( 6,48)( 7,47)( 8,13)(11,42)(12,41)(14,26)(15,46)(16,44)(17,36)(18,33)(19,32)(20,34)(21,30)(22,35)(23,31)(24,29)(27,40)(28,39)(37,43)(38,45);
s2 := Sym(48)!( 1,46)( 2,40)( 3,39)( 4,36)( 5,48)( 6,11)( 7,12)( 8,44)( 9,24)(10,42)(13,21)(14,41)(15,29)(16,30)(17,27)(18,28)(19,31)(20,45)(22,34)(23,43)(25,33)(26,47)(32,37)(35,38);
poly := sub<Sym(48)|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, s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;

References