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.

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.

[3] Danzer's configuration DCD(4) is the fourth term of an infinite series of

In [4] configurations DCD(n) were further generalized to the unbalanced

Each DCD(2n,d) configuration is a subconfiguration of the

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.

The Levi graph of Danzer's configuration as unit distance graph .
The Hasse diagram of the set of all subsets of a three-element set {x, y, z}, ordered by inclusion. Distinct sets on the same horizontal layer are incomparable with each other. Two consecutive layers form a Levi graph of a suitable DCD-configuration.