Polytope of Type {10,12} with group SmallGroup(1920,240872)

Overview

Group: SmallGroup(1920,240872)
Rank: 3
Schläfli Type: {10,12}
Vertices, edges, …: 80, 480, 96
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

None in this Atlas.

Vertex figure of

None in this Atlas.

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

{5,3}*60

120-fold

{2,4}*16

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^5> of order 2

72 facets

48 of {5}*10
24 of {10}*20

40 vertex figures

40 of {12}*24

P/N, where N=<(s0*s1)^3*s2*s1*s0*s1*s2*s1> of order 3

32 facets

32 of {10}*20

32 vertex figures

24 of {12}*24
8 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.