In geometry, a truncated projective plane (TPP), also known as a dual affine plane, is a special kind of a hypergraph or geometric configuration that is constructed in the following way.[1][2]
Take a finite projective plane.
Remove one of the points (vertices) in the plane.
Remove all lines (edges) containing that point.
These objects have been studied in many different settings, often independent of one another, and so, many terminologies have been developed. Also, different areas tend to ask different types of questions about these objects and are interested in different aspects of the same objects.
^Aharoni, Ron (2001-01-01). "Ryser's Conjecture for Tripartite 3-Graphs". Combinatorica. 21 (1): 1–4. doi:10.1007/s004930170001. ISSN 0209-9683. S2CID 13307018.
^Füredi, Zoltán (1989-05-01). "Covering the complete graph by partitions". Discrete Mathematics. 75 (1): 217–226. doi:10.1016/0012-365X(89)90088-5. ISSN 0012-365X.
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when n = r – 1 is a prime power, and all colors are edges of the truncatedprojectiveplane of order n. So each color has n2 = rn – r + 1 edges and a fractional...
dodecahedron Truncated rhombic dodecahedron 24-cell – 4D analog of rhombic dodecahedron Archimede construction systems Fully truncated rhombic dodecahedron...
of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes...
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