Английская Википедия:Danzer's configuration
In mathematics, Danzer's configuration is a self-dual configuration of 35 lines and 35 points, having 4 points on each line and 4 lines through each point. It is named after the German geometer Ludwig Danzer and was popularised by Branko Grünbaum.Шаблон:Sfnp The Levi graph of the configuration is the Kronecker cover of the odd graph O4,Шаблон:Sfnp and is isomorphic to the middle layer graph of the seven-dimensional hypercube graph Q7. The middle layer graph of an odd-dimensional hypercube graph Q2n+1(n,n+1) is a subgraph whose vertex set consists of all binary strings of length 2n + 1 that have exactly n or n + 1 entries equal to 1, with an edge between any two vertices for which the corresponding binary strings differ in exactly one bit. Every middle layer graph is Hamiltonian.Шаблон:Sfnp
Danzer's configuration DCD(4) is the fourth term of an infinite series of <math> (\tbinom {2n-1}{n}_n) </math> configurations DCD(n), where DCD(1) is the trivial configuration (11), DCD(2) is the trilateral (32) and DCD(3) is the Desargues configuration (103). In Шаблон:Sfnp configurations DCD(n) were further generalized to the unbalanced <math> (\tbinom {n}{d}_d, \tbinom {n}{d-1}_{n-d+1}) </math> configuration DCD(n,d) by introducing parameter d with connection DCD(n) = DCD(2n-1,n). DCD stands for Desargues-Cayley-Danzer. Each DCD(2n,d) configuration is a subconfiguration of the <math> (2^{2n}_{2n+1})</math> Clifford configuration. While each DCD(n,d) admits a realisation as a geometric point-line configuration, the Clifford configuration can only be realised as a point-circle configuration and depicts the Clifford's circle theorems.
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