Polytope of Type {14,8,2} with group SmallGroup(448,1207)

Overview

Group: SmallGroup(448,1207)
Rank: 4
Schläfli Type: {14,8,2}
Vertices, edges, …: 14, 56, 8, 2
Order of s₀s₁s₂s₃: 56
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

{14,4,2}*224

4-fold

{14,2,2}*112

7-fold

{2,8,2}*64

8-fold

{7,2,2}*56

14-fold

{2,4,2}*32

28-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

Permutation Representation (GAP)

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