Polytope of Type {2,6,28}

Atlas Canonical Name {2,6,28}*672b

Overview

Group: SmallGroup(672,1260)
Rank: 4
Schläfli Type: {2,6,28}
Vertices, edges, …: 2, 6, 84, 28
Order of s₀s₁s₂s₃: 42
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

7-fold

{2,6,4}*96b

14-fold

{2,3,4}*48

Covers minimal covers in bold

2-fold

{2,6,28}*1344

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29);;
s2 := ( 5, 6)( 7,27)( 8,28)( 9,30)(10,29)(11,23)(12,24)(13,26)(14,25)(15,19)(16,20)(17,22)(18,21);;
s3 := ( 3,10)( 4, 9)( 5, 8)( 6, 7)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(30)!(1,2);
s1 := Sym(30)!( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29);
s2 := Sym(30)!( 5, 6)( 7,27)( 8,28)( 9,30)(10,29)(11,23)(12,24)(13,26)(14,25)(15,19)(16,20)(17,22)(18,21);
s3 := Sym(30)!( 3,10)( 4, 9)( 5, 8)( 6, 7)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21);
poly := sub<Sym(30)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3 >;