Geodesic
Omittable planes
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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In analogy to omittable lines in the plane, we initiate the study of omittable planes in $3$-space. Given a collection of $n$ planes in real projective $3$-space, a plane $\Pi$ is said to be omittable if $\Pi$ is free of ordinary lines of intersection – in other words, if all the lines of intersection of $\Pi$ with other planes from the collection come at the intersection of three or more planes. We provide two infinite families of planes yielding omittable planes in either a pencil or near-pencil, together with examples having between three and seven omittable planes, examples that we call "sporadic," which do not fit into either of the two infinite families.
DOI : 10.37236/662
Classification : 52C35
Mots-clés : omittable planes, aggregate, arrangement 
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     author = {Branko Gr\"unbaum and Jonathan Lenchner},
     title = {Omittable planes},
     journal = {The electronic journal of combinatorics},
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     number = {1},
     doi = {10.37236/662},
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Branko Grünbaum; Jonathan Lenchner. Omittable planes. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/662

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