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In finite geometry, PG(3,2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane.It has 15 points, 35 lines, and 15 planes. It also has the following properties: * Each point is contained in 7 lines and 7 planes * Each line is contained in 3 planes and contains 3 points * Each plane contains 7 points and 7 lines * Each plane is isomorphic to the Fano plane * Every pair of distinct planes intersect in a line * A line and a plane not containing the line intersect in exactly one point

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  • PG(3,2) (en)
  • PG(3,2) (ru)
  • PG(3,2) (uk)
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  • In finite geometry, PG(3,2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane.It has 15 points, 35 lines, and 15 planes. It also has the following properties: * Each point is contained in 7 lines and 7 planes * Each line is contained in 3 planes and contains 3 points * Each plane contains 7 points and 7 lines * Each plane is isomorphic to the Fano plane * Every pair of distinct planes intersect in a line * A line and a plane not containing the line intersect in exactly one point (en)
  • PG(3,2) — это наименьшее трёхмерное проективное пространство, которое можно рассматривать как расширение плоскости Фано.Пространство имеет 15 точек, 35 прямых и 15 плоскостей. Оно имеет также следующие свойства: * Каждая точка принадлежит 7 прямым и 7 плоскостям * Каждая прямая содержится в 3 плоскостях и содержит 3 точки * Каждая плоскость содержит 7 точек и 7 прямых * Каждая плоскость изоморфна плоскости Фано * Любая пара различных плоскостей пересекаются по прямой * Прямая и плоскость, не содержащая прямую, имеют в точности одну общую точку (ru)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/150614-PG-3-2-schoolgirls-arrangement.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/GQ(2,2).svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Fano_Space.png
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  • In finite geometry, PG(3,2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane.It has 15 points, 35 lines, and 15 planes. It also has the following properties: * Each point is contained in 7 lines and 7 planes * Each line is contained in 3 planes and contains 3 points * Each plane contains 7 points and 7 lines * Each plane is isomorphic to the Fano plane * Every pair of distinct planes intersect in a line * A line and a plane not containing the line intersect in exactly one point (en)
  • PG(3,2) — это наименьшее трёхмерное проективное пространство, которое можно рассматривать как расширение плоскости Фано.Пространство имеет 15 точек, 35 прямых и 15 плоскостей. Оно имеет также следующие свойства: * Каждая точка принадлежит 7 прямым и 7 плоскостям * Каждая прямая содержится в 3 плоскостях и содержит 3 точки * Каждая плоскость содержит 7 точек и 7 прямых * Каждая плоскость изоморфна плоскости Фано * Любая пара различных плоскостей пересекаются по прямой * Прямая и плоскость, не содержащая прямую, имеют в точности одну общую точку (ru)
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