Overview
- Group
- SmallGroup(648,703)
- Rank
- 3
- Schläfli Type
- {4,9}
- Vertices, edges, …
- 36, 162, 81
- Order of s0s1s2
- 9
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
27-fold
Covers minimal covers in bold
2-fold
3-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*s2*s1)^2*s0*(s1*s2)^2> of order 3
27 facets
- 27 of {4}*8
12 vertex figures
- 12 of {9}*18
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26);; s1 := ( 2, 3)( 4,19)( 5,21)( 6,20)( 7,10)( 8,12)( 9,11)(13,25)(14,27)(15,26)(17,18)(23,24);; s2 := ( 1, 4)( 2,22)( 3,13)( 5,19)( 6,10)( 8,25)( 9,16)(11,24)(12,15)(14,21)(17,27)(20,23);; 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*s1*s2*s0*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(27)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26); s1 := Sym(27)!( 2, 3)( 4,19)( 5,21)( 6,20)( 7,10)( 8,12)( 9,11)(13,25)(14,27)(15,26)(17,18)(23,24); s2 := Sym(27)!( 1, 4)( 2,22)( 3,13)( 5,19)( 6,10)( 8,25)( 9,16)(11,24)(12,15)(14,21)(17,27)(20,23); poly := sub<Sym(27)|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*s1*s2*s0*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.