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Red article:

Take the partitions of {1, 2,..., 2n+2} into n+1 2-subsets as points and the partitions into n 2-subsets and one 4-subset as lines. A point is incident to a line if as a partition it is a refinement of the line.

Read paper:

Let n∈N. With every set X of size 2n+2, there is associated a point-line geometry ${\displaystyle H_{n}(X)}$: the points of ${\displaystyle H_{n}(X)}$ are the partitions of X in n+1 subsets of size 2; the lines of ${\displaystyle H_{n}(X)}$ are the partitions of X in n−1 subsets of size 2 and 1 subset of size 4; a point p of ${\displaystyle H_{n}(X)}$ is incident with a line L of ${\displaystyle H_{n}(X)}$ if and only if the partition corresponding to p is a refinement of the partition corresponding to L.

So, must be n or n-1? Jumpow ( talk) 09:02, 21 August 2017 (UTC) reply

Read:

out that regular near 2d-gons are precisely those near 2d-gons whose point graph is a distance-regular graph.

This term have to be explained (with definition, with link to other article or by reference to book). Jumpow ( talk) 11:57, 21 August 2017 (UTC) reply