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The Fano plane is an example of an (n 3)-configuration, that is, a set of n points and n lines with three points on each line and three lines through each point. The Fano plane, a (7 3)-configuration, is unique and is the smallest such configuration. [11]
The Fano plane, discussed below, is denoted by PG(2, 2). The third example above is the projective plane PG(2, 3). The Fano plane. Points are shown as dots; lines are shown as lines or circles. The Fano plane is the projective plane arising from the field of two elements. It is the smallest projective plane, with only seven points and seven lines.
A complete list of all 480 octonions and their Fano plane and multiplication tables (in two parts) are here and here. (.pdf 80MB each). (.pdf 80MB each). A description of the Mathematica algorithm with code is here .
The colored version is now at File:Fano plane with colored lines.svg. 02:04, 8 May 2021: 512 × 512 (1 KB) Cmglee: Colour lines and points. 15:11, 13 January 2021:
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The Fano plane is the projective plane with the fewest points and lines. The smallest 2-dimensional projective geometry (that with the fewest points) is the Fano plane, which has 3 points on every line, with 7 points and 7 lines in all, having the following collinearities:
A complete list of all 480 octonions and their Fano plane and multiplication tables (.pdf 30MB) Date: 7 March 2013, 19:39:41: Source: Own work: Author: Jgmoxness ...
Fano plane with numbered points. Incidence structure of the Fano plane. Compare: Z2^3; Lattice of subgroups Hasse diagram.svg: This SVG was created with Inkscape.