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In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations of the sphere – and toroidal polyhedra – tessellations of the toroids. As cellular decompositions of the projective plane, they have Euler characteristic 1, while spherical polyhedra have Euler characteristic 2. The qualifier "globally" is to contrast with locally projective polyhedra, which are in the theory of abstract polyhedra.

Attributes	Values
rdfs:label	Projective polyhedron (en)
rdfs:comment	In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations of the sphere – and toroidal polyhedra – tessellations of the toroids. As cellular decompositions of the projective plane, they have Euler characteristic 1, while spherical polyhedra have Euler characteristic 2. The qualifier "globally" is to contrast with locally projective polyhedra, which are in the theory of abstract polyhedra. (en)
foaf:depiction
dcterms:subject	Projective polyhedra
Wikipage page ID	26952055 (xsd:integer)
Wikipage revision ID	1119491072 (xsd:integer)
Link from a Wikipage to another Wikipage	Cuboctahedron Tetrahemihexahedron 11-cell Commutative square Convex polyhedra Elliptic geometry Galois connection Geometry Convex combination Reflection through the origin Density (polytope) Projective polyhedra Fundamental domain Hemi-dodecahedron Hemi-icosahedron Hemi-octahedron Pin group Projective orthogonal group Spin group Hosohedra Central extension (mathematics) Local homeomorphism Abstract polyhedra Euclidean space Abstract vertex figure Journal of Combinatorial Theory Tessellation Polyhedral compound Hemicube (geometry) Isometries Abstract polytope Aequationes Mathematicae Binary polyhedral group Toroidal polyhedron Dihedral group CW complex Platonic solid Sphere Spherical polyhedra Real projective plane Lattice theorem Stellated octahedron Euler characteristic Dihedra Immersion (mathematics) Spherical polyhedron Uniform polyhedra Roman surface Simply connected Toroidal polyhedra Central symmetry Centrally symmetric Covering map Antipodal map Hemipolyhedra Local isometry Spherical tiling
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=JfmlMYe6MJgC&pg=PA162 https://books.google.com/books%3Fid=E_HCwwxMbfMC&pg=PA34 https://books.google.com/books%3Fid=d6sBd9h1HbMC&pg=PA147 https://books.google.com/books%3Fid=fcm-YW5WqWwC&lpg=PA43 http://portal.acm.org/citation.cfm%3Fid=158410
sameAs	Projective polyhedron Projective polyhedron Projective polyhedron Projective polyhedron
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has abstract	In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations of the sphere – and toroidal polyhedra – tessellations of the toroids. Projective polyhedra are also referred to as elliptic tessellations or elliptic tilings, referring to the projective plane as (projective) elliptic geometry, by analogy with spherical tiling, a synonym for "spherical polyhedron". However, the term elliptic geometry applies to both spherical and projective geometries, so the term carries some ambiguity for polyhedra. As cellular decompositions of the projective plane, they have Euler characteristic 1, while spherical polyhedra have Euler characteristic 2. The qualifier "globally" is to contrast with locally projective polyhedra, which are in the theory of abstract polyhedra. Non-overlapping projective polyhedra (density 1) correspond to spherical polyhedra (equivalently, convex polyhedra) with central symmetry. This is elaborated and extended below in and . (en)
gold:hypernym	Tessellation
prov:wasDerivedFrom	wikipedia-en:Projective_polyhedron?oldid=1119491072&ns=0
page length (characters) of wiki page	16478 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Projective_polyhedron
is Link from a Wikipage to another Wikipage of	List of regular polytopes and compounds Cube Elliptic tiling List of mathematical shapes List of polygons, polyhedra and polytopes Tetrahemihexahedron 11 (number) Projective polyhedra Hemi-cuboctahedron Hemi-dodecahedron

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