Overview
- Group
- SmallGroup(432,521)
- Rank
- 3
- Schläfli Type
- {6,36}
- Vertices, edges, …
- 6, 108, 36
- Order of s0s1s2
- 9
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
18-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35);; s1 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,29)(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(21,33)(22,34)(23,36)(24,35);; s2 := ( 1,16)( 2,15)( 3,14)( 4,13)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(25,32)(26,31)(27,30)(28,29)(33,36)(34,35);; 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*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35); s1 := Sym(36)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,29)(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(21,33)(22,34)(23,36)(24,35); s2 := Sym(36)!( 1,16)( 2,15)( 3,14)( 4,13)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(25,32)(26,31)(27,30)(28,29)(33,36)(34,35); poly := sub<Sym(36)|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*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.