Polytope of Type {14,4} with group SmallGroup(112,31)

Overview

Group: SmallGroup(112,31)
Rank: 3
Schläfli Type: {14,4}
Vertices, edges, …: 14, 28, 4
Order of s₀s₁s₂: 28
Order of s₀s₁s₂s₁: 2
Also known as: {14,4|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{14,2}*56

4-fold

{7,2}*28

7-fold

{2,4}*16

14-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

14-fold

15-fold

16-fold

17-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)(20,21)(22,26)(24,27);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)(19,23)(20,24)(25,27)(26,28);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*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*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(28)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28);
s1 := Sym(28)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)(20,21)(22,26)(24,27);
s2 := Sym(28)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)(19,23)(20,24)(25,27)(26,28);
poly := sub<Sym(28)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*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*s0*s1 >;

References