Polytope of Type {2,28,4} with group SmallGroup(448,940)

Overview

Group: SmallGroup(448,940)
Rank: 4
Schläfli Type: {2,28,4}
Vertices, edges, …: 2, 28, 56, 4
Order of s₀s₁s₂s₃: 28
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

4-fold

{2,14,2}*112

7-fold

{2,4,4}*64

8-fold

{2,7,2}*56

14-fold

28-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(31,45)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,52)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53);;
s2 := ( 3,32)( 4,31)( 5,37)( 6,36)( 7,35)( 8,34)( 9,33)(10,39)(11,38)(12,44)(13,43)(14,42)(15,41)(16,40)(17,46)(18,45)(19,51)(20,50)(21,49)(22,48)(23,47)(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54);;
s3 := (31,38)(32,39)(33,40)(34,41)(35,42)(36,43)(37,44)(45,52)(46,53)(47,54)(48,55)(49,56)(50,57)(51,58);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(58)!(1,2);
s1 := Sym(58)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(31,45)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,52)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53);
s2 := Sym(58)!( 3,32)( 4,31)( 5,37)( 6,36)( 7,35)( 8,34)( 9,33)(10,39)(11,38)(12,44)(13,43)(14,42)(15,41)(16,40)(17,46)(18,45)(19,51)(20,50)(21,49)(22,48)(23,47)(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54);
s3 := Sym(58)!(31,38)(32,39)(33,40)(34,41)(35,42)(36,43)(37,44)(45,52)(46,53)(47,54)(48,55)(49,56)(50,57)(51,58);
poly := sub<Sym(58)|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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;