Polytope of Type {12,10} with group SmallGroup(960,10889)

Overview

Group: SmallGroup(960,10889)
Rank: 3
Schläfli Type: {12,10}
Vertices, edges, …: 48, 240, 40
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

{12,10,2} ·1920

Vertex figure of

{2,12,10} ·1920

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

{3,5}*60

120-fold

{2,2}*8

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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