Overview
- Group
- SmallGroup(432,741)
- Rank
- 3
- Schläfli Type
- {6,4}
- Vertices, edges, …
- 54, 108, 36
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
6-fold
9-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
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)^3*s2*(s1*s0)^2*s1*s2> of order 2
18 facets
- 18 of {6}*12
27 vertex figures
- 27 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 3
12 facets
- 12 of {6}*12
18 vertex figures
- 18 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 3
12 facets
- 12 of {6}*12
18 vertex figures
- 18 of {4}*8
P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2> of order 4
12 facets
15 vertex figures
P/N, where N=<(s0*s1)^3, s1*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 6
9 facets
9 vertex figures
- 9 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2> of order 6
6 facets
- 6 of {6}*12
12 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 9
6 facets
6 vertex figures
- 6 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);; s1 := ( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12);; s2 := (4,7)(5,8)(6,9);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(18)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17); s1 := Sym(18)!( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12); s2 := Sym(18)!(4,7)(5,8)(6,9); poly := sub<Sym(18)|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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.