Polytope of Type {4,42} with group SmallGroup(1680,927)

Overview

Group: SmallGroup(1680,927)
Rank: 3
Schläfli Type: {4,42}
Vertices, edges, …: 20, 420, 210
Order of s₀s₁s₂: 35
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

7-fold

{4,6}*240c

14-fold

{4,6}*120

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*s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 2

105 facets

105 of {4}*8

10 vertex figures

10 of {42}*84

P/N, where N=<s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s2> of order 2

112 facets

98 of {4}*8
14 of {2}*4

10 vertex figures

10 of {42}*84

P/N, where N=<(s0*s1)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 4

63 facets

21 of {2}*4
42 of {4}*8

5 vertex figures

5 of {42}*84

Representations

Permutation Representation (GAP)

s0 := (10,12);;
s1 := ( 2, 3)( 4, 5)( 6, 7)( 9,10)(11,12);;
s2 := (1,2)(3,4)(5,6)(8,9);;
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*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(12)!(10,12);
s1 := Sym(12)!( 2, 3)( 4, 5)( 6, 7)( 9,10)(11,12);
s2 := Sym(12)!(1,2)(3,4)(5,6)(8,9);
poly := sub<Sym(12)|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*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.