#11703: another example of simplicial complex : the K3 surface
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Reporter: chapoton | Owner: jhpalmieri
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.7.2
Component: algebraic topology | Keywords: simplicial complex
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by chapoton):
Here is the code with the group (of size 240) and the orbit closure. The
other option is just a long list.
{{{
def K3_surface():
"""
Returns the minimal triangulation of the K3 surface. This is a
simplicial complex with 16 vertices and 288 facets.
EXAMPLES::
sage: K3=simplicial_complexes.K3_surface() ; K3
Simplicial complex with vertex set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16) and 288 facets
sage: K3.f_vector()
[1, 16, 120, 560, 720, 288]
REFERENCES:
- Combinatorial properties of the K3 surface: Simplicial blowups
and slicings by Jonathan Spreer & Wolfgang Kühnel
- M. Casella and W. K¨uhnel, A triangulated K3 surface with the
minimum number of vertices, Topology 40 (2001), 753–772.
"""
G =
PermutationGroup([[(1,3,8,4,9,16,15,2,14,12,6,7,13,5,10)],[(1,11,16),(2,10,14),(3,12,13),(4,9,15),(5,7,8)]])
gen1=(1,2,3,8,12)
gen2=(1,2,5,8,14)
liste=[tuple([g(i) for i in gen1]) for g in G]+[tuple([g(i) for i in
gen2]) for g in G]
return SimplicialComplex(liste)
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11703#comment:3>
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