Polytope of Type {14,10} with group SmallGroup(280,36)

Overview

Group: SmallGroup(280,36)
Rank: 3
Schläfli Type: {14,10}
Vertices, edges, …: 14, 70, 10
Order of s₀s₁s₂: 70
Order of s₀s₁s₂s₁: 2
Also known as: {14,10|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

5-fold

{14,2}*56

7-fold

{2,10}*40

10-fold

{7,2}*28

14-fold

{2,5}*20

35-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

Irregular Quotients of which this is a minimal cover

None.

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)(58,63)(59,62)(60,61)(65,70)(66,69)(67,68);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8,30)( 9,29)(10,35)(11,34)(12,33)(13,32)(14,31)(15,23)(16,22)(17,28)(18,27)(19,26)(20,25)(21,24)(36,37)(38,42)(39,41)(43,65)(44,64)(45,70)(46,69)(47,68)(48,67)(49,66)(50,58)(51,57)(52,63)(53,62)(54,61)(55,60)(56,59);;
s2 := ( 1,43)( 2,44)( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,64)(16,65)(17,66)(18,67)(19,68)(20,69)(21,70)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,63)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56);;
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*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*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(70)!( 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)(58,63)(59,62)(60,61)(65,70)(66,69)(67,68);
s1 := Sym(70)!( 1, 2)( 3, 7)( 4, 6)( 8,30)( 9,29)(10,35)(11,34)(12,33)(13,32)(14,31)(15,23)(16,22)(17,28)(18,27)(19,26)(20,25)(21,24)(36,37)(38,42)(39,41)(43,65)(44,64)(45,70)(46,69)(47,68)(48,67)(49,66)(50,58)(51,57)(52,63)(53,62)(54,61)(55,60)(56,59);
s2 := Sym(70)!( 1,43)( 2,44)( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,64)(16,65)(17,66)(18,67)(19,68)(20,69)(21,70)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,63)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56);
poly := sub<Sym(70)|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*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*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 >;

References