Polytope of Type {6,21} with group SmallGroup(252,36)

Overview

Group: SmallGroup(252,36)
Rank: 3
Schläfli Type: {6,21}
Vertices, edges, …: 6, 63, 21
Order of s₀s₁s₂: 42
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{2,21}*84

7-fold

{6,3}*36

9-fold

{2,7}*28

21-fold

{2,3}*12

Covers minimal covers in bold

2-fold

{6,42}*504c

3-fold

4-fold

5-fold

{6,105}*1260

6-fold

7-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63);;
s1 := ( 1,22)( 2,28)( 3,27)( 4,26)( 5,25)( 6,24)( 7,23)( 8,36)( 9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,29)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(44,49)(45,48)(46,47)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58);;
s2 := ( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,58)(37,57)(38,63)(39,62)(40,61)(41,60)(42,59);;
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*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(63)!(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63);
s1 := Sym(63)!( 1,22)( 2,28)( 3,27)( 4,26)( 5,25)( 6,24)( 7,23)( 8,36)( 9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,29)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(44,49)(45,48)(46,47)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58);
s2 := Sym(63)!( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,58)(37,57)(38,63)(39,62)(40,61)(41,60)(42,59);
poly := sub<Sym(63)|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*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;

References