The term projective polyhedron does not appear to be widely recognized as a distinct, established concept in the mainstream mathematical literature. Comprehensive encyclopedic sources, such as standard textbooks on polyhedral theory, projective geometry, or major mathematical reference works, do not contain a dedicated entry for this term.
Possible interpretations
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Polyhedron in projective space – In geometry, one may consider the analogue of a polyhedron when the ambient space is a real or complex projective space rather than Euclidean space. Such objects could be described as “polyhedra in projective space” or “projective polyhedral surfaces,” but no standard definition under the exact phrase “projective polyhedron” is documented.
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Quotient of a polyhedron by antipodal identification – Some authors have informally referred to the image of a centrally symmetric polyhedron under the identification of antipodal points (i.e., the passage from the sphere S² to the real projective plane ℝP²) as a “projective polyhedron.” This usage is occasional and not standardized.
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Historical or niche usage – A limited number of research articles and conference proceedings may employ the phrase in specific contexts (e.g., combinatorial topology, computational geometry) without providing a formal definition that has been adopted broadly.
Conclusion
Given the lack of a clear, widely accepted definition and the absence of reliable encyclopedic references, the term projective polyhedron remains insufficiently documented for an encyclopedic entry. Further investigation in specialized literature would be required to determine whether a more precise concept exists under this name.