Polytope of Type {10,6,3} with group SmallGroup(1080,287)

Overview

Group: SmallGroup(1080,287)
Rank: 4
Schläfli Type: {10,6,3}
Vertices, edges, …: 10, 90, 27, 9
Order of s₀s₁s₂s₃: 30
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{10,6|2},{6,3}₆}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

3-fold

{10,6,3}*360

5-fold

{2,6,3}*216

9-fold

{10,2,3}*120

15-fold

{2,6,3}*72

18-fold

{5,2,3}*60

45-fold

{2,2,3}*24

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=<(s1*s2)^2> of order 3

5 facets

3 of {10,2}*40
2 of {10,6}*120

10 vertex figures

10 of 3-fold non-regular quotient of {6,3}*108

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.