An informal description of the Ontology of the Fano Polytopes Knowledge Base developed so far.
All Fano Polytope instances belong to the owl:Class sd:FanoPolytope with predicates
that point to the remote resource.
The polymake files are in XML and there are some void tags for simple properties. These are listed here, with some (or even all) possible values (where … indicates that there are more values that are not listed):
REFLEXIVE : true
LINEALITY_DIM : 0
CONE_DIM : 6, 4, 5
N_INTERIOR_LATTICE_POINTS : 1
TERMINAL : false
SMOOTH : true
N_LATTICE_POINTS : 276, 90, 206, 71, 102, 331, 358, 55, 84, 233, 194, 259, 458,…
LATTICE : true
COMPRESSED : false
N_VERTICES : 32, 21, 26, 17, 18, 72, 30, 16, 44, 25, 28, 40, 14, 20, 24, …
CONE_AMBIENT_DIM : 6, 4, 5
N_EDGES : 35, 33, 32, 26, 48, 18, 30, 23, 29, 25, 27, 40, 41, 14, 20, …
SIMPLE : true
LATTICE_VOLUME : 10882, 4544, 5006, 331, 3606, 560, 5284, 7290, 2830, 5936, 6…
NORMAL : true
ESSENTIALLY_GENERIC : false, true
N_BOUNDARY_LATTICE_POINTS : 25, 27, 33, 30, 24, 29
GORENSTEIN_INDEX : 1
N_FACETS : 6, 11, 7, 9, 12, 14, 8, 4, 13, 10, 5
POINTED : true
VOLUME : 433/12, 1339/30, 32, 751/30, 185/6, 143/4, 99/4, 1169/30, 23…
FEASIBLE : true
CENTERED : true
SIMPLE_POLYHEDRON : true
CANONICAL : true
FACET_WIDTH : 4, 3, 7, 2, 5
GORENSTEIN : true
These void tags were converted to RDF predicates with namespace sdpt. (all lowercase like so “sdpt:gorenstein_index”). It is not clear yet if “pointed”, “feasible”, “centered”, etc… (those with “true” as only value) should be better modelled by introducing new (sub) classes. On the other hand there are also boolean properties that have “false” has value. If the class representation is chosen here, this would have to be modelled with a negative assertion.
A list of all predicates with number of occurences can be generated with a SPARQL-Query:
PREFIX sd: http://symbolicdata.org/Data/Model#
select distinct ?p count(?s)
where { ?s a sd:FanoPolytope . ?s ?p ?o .}
order by ?p
We list all properties with some comments:
These should probably be modeled as classes (along with the other “boolean” properties). Some additional input from the polytopes community is needed here.