The Number of (n3) Configurations
The number of nonisomorphic configurations of type (n3), starting at n = 7, is given by the sequence
- 1, 1, 3, 10, 31, 229, 2036, 21399, 245342, ... (sequence A001403 in OEIS)
These numbers count configurations as abstract incidence structures, regardless of realizability (Betten, Brinkmann & Pisanski 2000). As Gropp (1997) discusses, nine of the ten (103) configurations, and all of the (113) and (123) configurations, are realizable in the Euclidean plane, but for each n ≥ 16 there is at least one nonrealizable (n3) configuration. Gropp also points out a long-lasting error in this sequence: an 1895 paper attempted to list all (123) configurations, and found 228 of them, but the 229th configuration was not discovered until 1988.
Read more about this topic: Configuration (geometry)
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