Polytope of Type {56,2,2} with group SmallGroup(448,1193)

Overview

Group: SmallGroup(448,1193)
Rank: 4
Schläfli Type: {56,2,2}
Vertices, edges, …: 56, 56, 2, 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

{28,2,2}*224

4-fold

{14,2,2}*112

7-fold

{8,2,2}*64

8-fold

{7,2,2}*56

14-fold

{4,2,2}*32

28-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)(42,45)(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)(14,20)(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)(36,51)(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);;
s2 := (57,58);;
s3 := (59,60);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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*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*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(60)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)(42,45)(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);
s1 := Sym(60)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)(14,20)(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)(36,51)(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);
s2 := Sym(60)!(57,58);
s3 := Sym(60)!(59,60);
poly := sub<Sym(60)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*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*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*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 >;