Birkhoff Polytopes Ontology

An informal description of the Ontology of the Birkhoff Polytopes Knowledge Base developed so far.

Metadata and Semantics

All Birkhoff Polytope instances belong to the owl:Class sd:BirkhoffPolytope with predicates

• sd:hasPolymakeFile URI - the Resource file
• sd:hasEPSFile URI - the EPS file

that point to the remote resource.

The Birkhoff Polytope Fingerprint

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:BirkhoffPolytope . ?s ?p ?o .} order by ?p

We list all properties with some comments:

• sd:f-vector - a list of integers, e.g., “(16,40,44,26,8)”
• sd:hasCombinatorialType - some of sd:wed, sd:prod, sd:pyr, sd:join, sd:pyrb.
  • The deeper semantics has to be explained.
• sd:hasDescription - a description of the polytope, e.g., “wedge(join(edge,square))”
• sd:hasDimension integer - the dimension of the polytope, values within 2..8
• sd:hasNodes integer - values within 3..16
• sd:hasVertices integer - values within 3..256
• sd:hiCube integer - values within 1..8
• sd:simpl integer - values within 1..7