Projective plane

Description

Just a projective plane. Made of 6 vertices and 10 facets. (The vertices with the same label should be identified.)

Properties

Not constructible. Cohen-Macaulay over fields with characteristics except 2, but not otherwise. This example is partitionable.

Datum

projective.dat

Some table

vertex decomposable?	no
extendably shellable?	no
shellable?	no
constructible?	no
Cohen-Macaulay?	yes if the characteristics is not 2, but not otherwise.
partitionable?	yes
topology	Projective plane
f-vector	(1,6,15,10)
h-vector	(1,3,6,0)
made by	Everyone knows

References

see some introductory textbooks on topology.